example problem area of a triangle

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Pre-Algebra : Area of a Triangle

Study concepts, example questions & explanations for pre-algebra, all pre-algebra resources, example questions, example question #1 : area of a triangle.

The base is the side of the triangle that is intersected by the height.

$example problem area of a triangle$

Example Question #2 : Area Of A Triangle

$example problem area of a triangle$

Example Question #3 : Area Of A Triangle

$example problem area of a triangle$

The question is asking you to find the area of a right triangle.

First you must know the equation to find the area of a triangle,

$example problem area of a triangle$

A right triangle is special because the height and base are always the two smallest dimensions.

This makes the equation

$example problem area of a triangle$

Example Question #4 : Area Of A Triangle

What is the area of this shape?

$example problem area of a triangle$

From this shape we are able to see that we have a square and a triangle, so lets split it into the two shapes to solve the problem. We know we have a square based on the 90 degree angles placed in the four corners of our quadrilateral.

Since we know the first part of our shape is a square, to find the area of the square we just need to take the length and multiply it by the width. Squares have equilateral sides so we just take 5 times 5, which gives us 25 inches squared.

We now know the area of the square portion of our shape. Next we need to find the area of our right triangle. Since we know that the shape below the triangle is square, we are able to know the base of the triangle as being 5 inches, because that base is a part of the square's side.

To find the area of the triangle we must take the base, which in this case is 5 inches, and multipy it by the height, then divide by 2. The height is 3 inches, so 5 times 3 is 15. Then, 15 divided by 2 is 7.5.

We now know both the area of the square and the triangle portions of our shape. The square is 25 inches squared and the triangle is 7.5 inches squared. All that is remaining is to added the areas to find the total area. Doing this gives us 32.5 inches squared.

What is the area of the triangle?

Area of a triangle can be determined using the equation:

$example problem area of a triangle$

Bill paints a triangle on his wall that has a base parallel to the ground that runs from one end of the wall to the other. If the base of the wall is 8 feet, and the triangle covers 40 square feet of wall, what is the height of the triangle?

$example problem area of a triangle$

In order to find the area of a triangle, we multiply the base by the height, and then divide by 2.

$example problem area of a triangle$

Multiply both sides by two, which allows us to eliminate the two from the left side of our fraction.

The left-hand side simplifies to:

$example problem area of a triangle$

The right-hand side simplifies to:

$example problem area of a triangle$

Now our equation can be rewritten as:

$example problem area of a triangle$

Next we divide by 8 on both sides to isolate the variable:

$example problem area of a triangle$

Example Question #7 : Area Of A Triangle

A triangle has a height of 9 inches and a base that is one third as long as the height. What is the area of the triangle, in square inches?

$example problem area of a triangle$

None of these

$example problem area of a triangle$

The area of a triangle is found by multiplying the base times the height, divided by 2.

$example problem area of a triangle$

Given that the height is 9 inches, and the base is one third of the height, the base will be 3 inches.

$example problem area of a triangle$

We now have both the base (3) and height (9) of the triangle. We can use the equation to solve for the area.

$example problem area of a triangle$

The fraction cannot be simplified.

Example Question #8 : Area Of A Triangle

Example Question #9 : Area Of A Triangle

Given the following measurements of a triangle: base (b) and height (h), find the area.

$example problem area of a triangle$

The area of triangle is found using the formula

$example problem area of a triangle$

Provided with the base and the height, all we need to do is plug in the values and solve for A.

$example problem area of a triangle$

Since this is asking for the area of a shape, the units are squared.

$example problem area of a triangle$

Example Question #10 : Area Of A Triangle

$example problem area of a triangle$

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Area of triangles problems with solutions.

A set of problems on how to calculate the area of triangles using different formulas are presented along with detailed solutions .

Formulas for Area of Triangles

We first recall some of the most widely used formulas used to calculate the area of a triangle.

Formula 1 - Base and Height of a triangle are known

Area = (1 / 2) × base × height = (1 / 2) × AB × CD

Formula 2 - Two sides of a triangle and the angle between them are known

Formula 3 - three sides of a triangle are known, formula 4 - the three vertices of the triangle are known by their coordinates, problems on areas with solutions.

Problem 4 Find the area of an equilateral triangle wide length equal to 6 cm.

Solutions to the Above Problems

Solution to Problem 2 Triangle CDB has a base CD of length 20. Its height is the side AB of the triangle because it start from the vertex B opposite the base CD is perpendicular to AC and therefore to the base DC. Hence the use of formula 1 to find the area of triangle. Area = (1/2) × 20 × 80 = 40 unit 2

Solution to Problem 3 We are given two sides and the angle opposite one of the sides. One way to find the area is to find angle B and use formula 2. Use the sine law to write sin(A) / BC = sin(C) / AB which gives sin(A) = 6 sin(55°) / 5 A = sin -1 (6 sin(55°) / 5) = 79.4 ° We now determine angle B using that fact that the sum of all angles in a triangle to be 180 °. B = 180 - 55 - 79.4 = 45.6 ° Use formula 2 to find the area Area = (1 / 2) × 5 × 6 × sin(45.6 °) = 10.7 unit 2

Solution to Problem 8 The shape whose are is to be calculated is made up of two triangles ADC and ACB with a common side AC. The area of triangle ACB can be calculated using formula 2 (we know two sides and the angle between them). For triangle ADC ,we know two sides. We can find side AC using the cosine law . in triangle ACB as follows AC 2 = AB 2 + CB 2 - 2 (AB)(AC) cos (B) Substitute by the numerical values and calculate AC AC = √( 400 2 + 800 2 - 2 (400)(800) cos (45°) ) = 589.5 We may use Heron's formula since we know the three sides of triangle ADC Let s = (1/2)(AD + DC + CA) = (1/2)(245 + 432 + 589.5) = 633.25 Area of triangle ADC = √( s × (s - AD) × (s - DC) × (s - CA) ) = √( 633.25 × (633.25 - 245) × (633.25 - 432) × (633.25 - 589.5) ) = 46526 ft 2 Area of triangle ACB = (1 / 2) BA × BC × sin (B) = (1 / 2) 400 × 800 × sin (45°) = 113137 ft 2 Total area of the given shape is obtained by adding the areas of triangles ADC and ACB Area = 46526 + 113137 = 158663 ft 2

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Area of Triangle

Area of a triangle is the region enclosed by it, in a two-dimensional plane. As we know, a triangle is a closed shape that has three sides and three vertices. Thus, the area of a triangle is the total space occupied within the three sides of a triangle. The general formula to find the area of the triangle is given by half of the product of its base and height.

In general, the term “area” is defined as the region occupied inside the boundary of a flat object or figure. The measurement is done in square units with the standard unit being square meters (m 2 ). For the computation of area, there are predefined formulas for squares, rectangles, circles, triangles, etc. In this article, we will learn the area of triangle formulas for different types of triangles, along with some example problems.

What is the Area of a Triangle?

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h. Hence, to find the area of a tri-sided polygon, we have to know the base (b) and height (h) of it . It is applicable to all types of triangles , whether it is scalene, isosceles or equilateral. To be noted, the base and height of the triangle are perpendicular to each other. The unit of area is measured in square units (m 2 , cm 2 ).

Example: What is the area of a triangle with base b = 3 cm and height h = 4 cm?

Using the formula,

Area of a Triangle, A = 1/2 × b × h

= 1/2 × 4 (cm) × 3 (cm)

= 2 (cm) × 3 (cm)

Apart from the above formula, we have Heron’s formula to calculate the triangle’s area when we know the length of its three sides. Also, trigonometric functions are used to find the area when we know two sides and the angle formed between them in a triangle. We will calculate the area for all the conditions given here.

Area of a Triangle Formula

The area of the triangle is given by the formula mentioned below:

where b and h are the base and height of the triangle, respectively.

Now, let’s see how to calculate the area of a triangle using the given formula. The area formulas for all the different types of triangles, like an area of an equilateral triangle, right-angled triangle, an isosceles triangle along with how to find the area of a triangle with 3 sides using Heron’s formula with examples are given below.

Area of a Right Angled Triangle

A right-angled triangle, also called a right triangle has any one angle equal to 90°. Therefore, the height of the triangle will be the length of the perpendicular side.

Area of a Right Triangle = A = ½ × Base × Height (Perpendicular distance)

From the above figure,

Area of triangle ACB = 1/2 × a × b

Area of an Equilateral Triangle

An equilateral triangle is a triangle where all the sides are equal. The perpendicular drawn from the vertex of the triangle to the base divides the base into two equal parts. To calculate the area of the equilateral triangle , we have to know the measurement of its sides.

Area of an Equilateral Triangle = A = (√3)/4 × side 2

Area of an Isosceles Triangle

An isosceles triangle has two of its sides equal and also the angles opposite the equal sides are equal.

Area of Triangle with Three Sides (Heron’s Formula)

The area of a triangle with 3 sides of different measures can be calculated using Heron’s formula . Heron’s formula includes two important steps. The first step is to find the semi perimeter of a triangle by adding all three sides of a triangle and dividing it by 2. The next step is to apply the semi-perimeter of triangle value in the main formula called “Heron’s Formula” to find the area of a triangle.

Area of triangles for three sides-Heron's formula

We have seen that the area of special triangles could be obtained using the triangle formula. However, for a triangle with the sides being given, the calculation of height would not be simple. For the same reason, we rely on Heron’s Formula to calculate the area of the triangles with unequal lengths.

Area of a Triangle Given Two Sides and the Included Angle (SAS)

Now, the question comes, when we know the two sides of a triangle and an angle included between them, then how to find its area.

Let us take a triangle ABC, whose vertex angles are ∠A, ∠B, and ∠C, and sides are a,b and c, as shown in the figure below.

Now, if any two sides and the angle between them are given, then the formulas to calculate the area of a triangle is given by:

Area (∆ABC) = ½ bc sin A

Area (∆ABC) = ½ ab sin C

Area (∆ABC) = ½ ca sin B

These formulas are very easy to remember and also to calculate.

For example, If, in ∆ABC, A = 30° and b = 2, c = 4 in units. Then the area will be;

= ½ (2) (4) sin 30

= 4 x ½ (since sin 30 = ½)

= 2 sq.unit.

Area of a triangle solved examples.

Find the area of an acute triangle with a base of 13 inches and a height of 5 inches.

A = (½)× b × h sq.units

⇒ A = (½) × (13 in) × (5 in)

⇒ A = (½) × (65 in 2 )

⇒ A = 32.5 in 2

Find the area of a right-angled triangle with a base of 7 cm and a height of 8 cm.

A = (½) × b × h sq.units

⇒ A = (½) × (7 cm) × (8 cm)

⇒ A = (½) × (56 cm 2 )

⇒ A = 28 cm 2

Find the area of an obtuse-angled triangle with a base of 4 cm and a height 7 cm.

⇒ A = (½) × (4 cm) × (7 cm)

⇒ A = (½) × (28 cm 2 )

⇒ A = 14 cm 2

Frequently Asked Questions on Area of a Triangle

What is the area of a triangle, what is the area when two sides of a triangle and included angle are given, how to find the area of a triangle given three sides.

When the values of the three sides of the triangle are given, then we can find the area of that triangle by using Heron’s Formula. Refer to the section ‘ Area of a triangle by Heron’s formula ‘ mentioned in this article to get a complete idea.

How to find the area of a triangle using vectors?

Suppose vectors u and v are forming a triangle in space. Then, the area of this triangle is equal to half of the magnitude of the product of these two vectors, such that,

A = ½ |u × v|

How to calculate the area of a triangle?

For a given triangle, where the base of the triangle is b and height is h, the area of the triangle can be calculated by the formula, such as;

A = ½ (b × h) Square Unit

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

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13 Comments

I cleared all my doubts because of this explaination. thank you byjus for thissimple explaination.

how to find area of a triangle if sum of squares of sides is given?

Can I take hypotenuse as a base in a right angled triangle?

How to find the area of equilateral triangle if the median is x cm?

VERY NICE QUESTION

If height is not given in a triangle how to find area

you could use heron’s formula

awesome explanation byjus

This nice and really good app

how can u convert mm into cm millimetre into centimetre

To convert mm into cm, divide the given value by 10. 1 mm = 1/10 cm = 0.1 cm

find the area of equilateral triangle whose side is 4 cm

Area of equilateral triangle = √3/4a^2 If a = 4 cm, then, area = √3/4 (4)^2 = 6.93 sq.cm. (Approx.)

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Unit 8: Lesson 2

Area of triangles

Word Problems - Area of Triangles

These lessons, with videos, examples, step-by-step solutions and worksheets, help Algebra students learn how to solve word problems that involve area of triangles.

Writing quadratic equations to solve word problems: Area of a triangle

Example: The height of a triangle is 3 cm more than the base. The area of the triangle is 17 cm 2 . Find the base to the nearest hundredth of a cm.

How to solve a triangle if you know the area? This is a word problem you solve by writing an equation and factoring. Word Problem: Area of a Triangle

Example: The height of a triangle is 4 inches more than twice the length of the base. The area of the triangle is 35 square inches. Find the height of the triangle.

Area of a Triangle - Algebra and Geometry Help

Example: The base of triangle is 5 units less than twice the height. If the area is 75 square units, then what is the length of the base and the height?

Algebra and Triangles : solving equations linked to perimeter and area

Example: The sides of a triangle are given as 3x, x - 1 and 3x + 1. If the perimeter is 56m, find the area.

Find area of a triangle- word problem

Example: In triangle ABC, AD = 10cm, the length of CD is half the length of AD, and the length of BD is twice the length of AD. What is the area of triangle ABC?

How to find the dimensions of a triangle given its area? This problem would involving solving quadratic equations.

Example: The height of a triangle is 4 inches less than the length of the base. The area of the triangle is 30 in 2 . Find the height and the base.

Word problem involving area of triangle

Example: Before she goes camping, La Verne has to buy a tent pole to replace the one she lost on her last outing. If the area of the front of the tent is 22 square feet and the base of the tent has the dimensions indicated below, how tall must the pole be?

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How to find the Area of a Triangle

To find the area of a triangle, use the following formula

The area of a triangle is always half the product of the height and base.

$ Area = \frac{1}{2} (base \cdot height) $

So which side is the base?

Identify the base of a triangle in area formula

Any side of the triangle can be a base. All that matters is that the base and the height must be perpendicular.

Any side can be a base, but every base has only one height. The height is the line from the opposite vertex and perpendicular to the base. The illustration below shows how any leg of the triangle can be a base and the height always extends from the vertex of the opposite side and is perpendicular to the base. Play around with our applet to see how the area of a triangle can be computed from any base/height pairing.

The picture below shows you that the height can actually extend outside of the triangle . So technically the height does not necessarily intersect with the base.

Derivation of the Area of a Triangle from Rectangle

What is the area of the triangle pictured below?

Use the formula above.

$$ A = \frac{1}{2} (base \cdot height) \\ A = \frac{1}{2} (10 \cdot 3) \\ = \frac{1}{2} (30) \\ = \frac{30}{2} = 15 $$

Practice Problems

Find the area of each triangle below. Round each answer to the nearest tenth of a unit .

What is the area of the triangle in the following picture?

To find the area of the triangle on the left, substitute the base and the height into the formula for area .

$$ Area = \frac{1}{2} (base \cdot height) \\ =\frac{1}{2} (3 \cdot 3) \\ = \frac{1}{2} (9) \\ =\frac{9}{2} \\ = 4.5 \text{ inches squared} $$

Calculate the area of the triangle pictured below.

$$ Area = \frac{1}{2} (base \cdot height) \\ =\frac{1}{2} (24 \cdot 27.6) \\ = 331.2 \text{ inches squared} $$

$$ Area = \frac{1}{2} (base \cdot height) \\ =\frac{1}{2} (12 \cdot 2.5) \\ = 15 \text{ inches squared} $$

$$ Area = \frac{1}{2} (base \cdot height) \\ =\frac{1}{2} (12 \cdot 3.9) \\ = 23.4 \text{ inches squared} $$

$$ Area = \frac{1}{2} (base \cdot height) \\ =\frac{1}{2} (14 \cdot 4) \\ = 28 \text{ inches squared} $$

What is the area of the following triangle?

This problems involves 1 small twist. You must decide which of the 3 bases to use . Just remember that base and height are perpendicular. Therefore, the base is '11' since it is perpendicular to the height of 13.4.

$$ Area = \frac{1}{2} (base \cdot height) \\ =\frac{1}{2} (11 \cdot 13.4) \\ = 73.7 \text{ inches squared} $$

This problems involves 1 small twist. You must decide which of the 3 bases to use . Just remember that base and height are perpendicular. Therefore, the base is '12' since it is perpendicular to the height of 5.9.

$$ Area = \frac{1}{2} (base \cdot height) \\ =\frac{1}{2} (12 \cdot 5.9) \\ = 35.4 \text{ inches squared} $$

Like the last problem, you must decide which of the 3 bases to use . Just remember that base and height are perpendicular. Therefore, the base is '4' since it is perpendicular to the height of 17.7.

$$ Area = \frac{1}{2} (base \cdot height) \\ =\frac{1}{2} (4 \cdot 17.7) \\ = 35.4 \text{ inches squared} $$

Again, you must decide which of the 3 bases to use . Just remember that base and height are perpendicular. Therefore, the base is '22' since it is perpendicular to the height of 26.8.

$$ Area = \frac{1}{2} (base \cdot height) \\ =\frac{1}{2} (22 \cdot 26.8) \\ = 294.8 \text{ inches squared} $$

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Area of Triangles

There are several ways to find the area of a triangle.

Knowing Base and Height

When we know the base and height it is easy.

It is simply half of b times h

Area = 1 2 bh

(The Triangles page explains more)

The most important thing is that the base and height are at right angles. Have a play here:

Example: What is the area of this triangle?

Height = h = 12

Base = b = 20

Area = ½ bh = ½ × 20 × 12 = 120

Knowing Three Sides

There's also a formula to find the area of any triangle when we know the lengths of all three of its sides.

This can be found on the Heron's Formula page.

Knowing Two Sides and the Included Angle

When we know two sides and the included angle (SAS), there is another formula (in fact three equivalent formulas) we can use.

Depending on which sides and angles we know, the formula can be written in three ways:

Area = 1 2 ab sin C

Area = 1 2 bc sin A

Area = 1 2 ca sin B

They are really the same formula, just with the sides and angle changed.

Example: Find the area of this triangle:

First of all we must decide what we know.

We know angle C = 25º, and sides a = 7 and b = 10.

So let's get going:

How to Remember

Just think "abc": Area = ½ a b sin C

It is also good to remember that the angle is always between the two known sides , called the "included angle".

How Does it Work?

We start with this formula:

Area = ½ × base × height

We know the base is c , and can work out the height:

Area = ½ × (c) × (b × sin A)

Which can be simplified to:

By changing the labels on the triangle we can also get:

One more example:

Example: Find How Much Land

Farmer Rigby owns a triangular piece of land.

The length of the fence AB is 150 m. The length of the fence BC is 231 m.

The angle between fence AB and fence BC is 123º.

How much land does Farmer Rigby own?

First of all we must decide which lengths and angles we know:

Farmer Rigby has 14,530 m 2 of land

Area of Triangle

The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h. This formula is applicable to all types of triangles, whether it is a scalene triangle, an isosceles triangle, or an equilateral triangle. It should be remembered that the base and the height of a triangle are perpendicular to each other.

In this lesson, we will learn the area of triangle formulas for different types of triangles, along with some examples.

What is the Area of a Triangle?

The area of a triangle is the region enclosed within the sides of the triangle. The area of a triangle varies from one triangle to another depending on the length of the sides and the internal angles. The area of a triangle is expressed in square units, like, m 2 , cm 2 , in 2 , and so on.

Triangle Definition

A triangle is a closed figure with 3 angles, 3 sides, and 3 vertices. It is one of the most basic shapes in geometry and is denoted by the symbol △. There are different types of triangles in math that are classified on the basis of their sides and angles.

Area of Triangle Formula

The area of a triangle can be calculated using various formulas. For example, Heron’s formula is used to calculate the triangle’s area, when we know the length of all three sides. Trigonometric functions are also used to find the area of a triangle when we know two sides and the angle formed between them. However, the basic formula that is used to find the area of a triangle is:

Area of triangle = 1/2 × base × height

Observe the following figure to see the base and height of a triangle.

Let us find the area of a triangle using this formula.

Example: What is the area of a triangle with base 'b' = 2 cm and height 'h' = 4 cm?

Solution: Using the formula: Area of a Triangle, A = 1/2 × b × h = 1/2 × 4 × 2 = 4 cm 2

Triangles can be classified based on their angles as acute, obtuse, or right triangles. They can be scalene, isosceles, or equilateral triangles when classified based on their sides. Let us learn about the other ways that are used to find the area of triangles with different scenarios and parameters.

Area of Triangle Using Heron's Formula

Heron's formula is used to find the area of a triangle when the length of the 3 sides of the triangle is known. To use this formula, we need to know the perimeter of the triangle which is the distance covered around the triangle and is calculated by adding the length of all three sides. Heron’s formula has two important steps.

Consider the triangle ABC with side lengths a, b, and c. To find the area of the triangle we use Heron's formula:

Area = $\sqrt {s(s - a)(s - b)(s - c)}$

Note that (a + b + c) is the perimeter of the triangle. Therefore, 's' is the semi-perimeter which is: (a + b + c)/2

Area of Triangle With 2 Sides and Included Angle (SAS)

When two sides and the included angle of a triangle are given, we use a formula that has three variations according to the given dimensions. For example, consider the triangle given below.

Area of triangle formula with 2 sides and an included angle

When sides 'b' and 'c' and included angle A is known, the area of the triangle is:

Area (∆ABC) = 1/2 × bc × sin(A)

When sides 'a' and 'b' and included angle C is known, the area of the triangle is:

Area (∆ABC) = 1/2 × ab × sin(C)

When sides 'a' and 'c' and included angle B is known, the area of the triangle is:

Area (∆ABC) = 1/2 × ac × sin(B)

Example: In ∆ABC, angle A = 30°, side 'b' = 4 units, side 'c' = 6 units.

Area (∆ABC) = 1/2 × bc × sin A

= 1/2 × 4 × 6 × sin 30º

= 12 × 1/2 (since sin 30º = 1/2)

Area = 6 square units.

How to Find the Area of a Triangle?

The area of a triangle can be calculated using various formulas depending upon the type of triangle and the given dimensions.

Area of Triangle Formulas

The area of triangle formulas for all the different types of triangles like the equilateral triangle, right-angled triangle , and isosceles triangle are given below.

Area of a Right-Angled Triangle

A right-angled triangle, also called a right triangle, has one angle equal to 90° and the other two acute angles sum up to 90°. Therefore, the height of the triangle is the length of the perpendicular side. The formula that is used in this case is:

Area of a Right Triangle = A = 1/2 × Base × Height

Area of an Equilateral Triangle

Area of an Equilateral Triangle = A = (√3)/4 × side 2

Area of an Isosceles Triangle

An isosceles triangle has two of its sides equal and the angles opposite the equal sides are also equal. The formula that is used in this case is:

Area of an Isosceles Triangle = A = $\frac{1}{4}b\sqrt {4{a^2} - {b^2}}$

where 'b' is the base and 'a' is the measure of one of the equal sides.

Area of Triangle when 3 Sides are Given

The area of a triangle can be calculated when 3 sides are given. In this scenario, we assume that all the 3 sides of the triangle are of different lengths. In other words, this is a scalene triangle and we use the Heron's formula to find the area of the triangle. The Heron's formula is explained above on this page and is expressed as follows: Area of triangle = $\sqrt {s(s - a)(s - b)(s - c)}$ where a, b, and c are the sides of the triangle and 's' is the semi-perimeter; s = (a + b + c)/2.

Observe the table given below which summarizes all the formulas for the area of a triangle.

Area of Triangle Examples

Example 1: Find the area of a triangle with a base of 10 inches and a height of 5 inches.

Let us find the area using the area of triangle formula:

Area of triangle = (1/2) × b × h

A = 1/2 × 10 × 5

A = 1/2 × 50

Therefore, the area of the triangle (A) = 25 in 2

Example 2: Find the area of an equilateral triangle with a side of 2 cm.

We can calculate the area of an equilateral triangle using the area of triangle formula, Area of an equilateral triangle = (√3)/4 × side 2 where 'a' is the length of one equal side. On substituting the values, we get, Area of an equilateral triangle = (√3)/4 × 2 2

Example 3: Find the area of a triangle with a base of 8 cm and a height of 7 cm.

A = 1/2 × 8 × 7

A = 1/2 × 56

A = 28 cm 2

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Practice Questions on Area of Triangle

Faqs on area of triangle.

The area of a triangle is the space enclosed within the three sides of a triangle. It is calculated with the help of various formulas depending on the type of triangle and is expressed in square units like, cm 2 , inches 2 , and so on.

What is the Area of Triangle Formula?

The basic formula to find the area of a triangle is, area of triangle = 1/2 (b × h); where 'b' is the base and 'h' is the height of the triangle . However, there are other formulas that are used to find the area of a triangle which depend upon the type of triangle and the known dimensions.

The area of a triangle can be calculated if the base and height of the triangle is given. The basic formula that is used to calculate the area is, Area of triangle = 1/2 (base × height). In other scenarios, when other parameters are known, the following formulas are used to find the area of a triangle:

How to Find the Base and Height of a Triangle?

The area of the triangle is calculated with the formula: A = 1/2 (base × height). Using the same formula, the height or the base can be calculated when the other dimensions are known. For example, if the area and the base of the triangle is known then the height can be calculated as, Height of the triangle = (2 × Area)/base. Similarly, when the height and the area is known, the base can be calculated with the formula, Base of the triangle = (2 × Area)/height

How to Find the Area and Perimeter of a Triangle?

The area of a triangle can be calculated with the help of the formula: A = 1/2 (b × h). The perimeter of a triangle can be calculated by adding the lengths of all the three sides of the triangle.

How to Find the Area of a Triangle Without Height?

The area of a triangle can be calculated when only the length of the 3 sides of the triangle are known and the height is not given. In this case, the Heron's formula can be used to find the area of the triangle. Heron's formula: A = $\sqrt {s(s - b)(s - b)(s - c)}$ where a, b, and c are the sides of the triangle and 's' is the semi-perimeter; s = (a + b + c)/2.

How to Find the Area of Triangle with Two Sides and an Included Angle?

In a triangle, when two sides and the included angle is given, then the area of the triangle is half the product of the two sides and sine of the included angle. For example, In ∆ABC, when sides 'b' and 'c' and included angle A is known, the area of the triangle is calculated with the help of the formula: 1/2 × b × c × sin(A). For a detailed explanation refer to the section, 'Area of Triangle With 2 Sides and Included Angle ( SAS )', given on this page.

How to Find the Area of a Triangle with 3 Sides?

The area of a triangle with 3 sides can be calculated using Heron's formula. Heron's formula: A = $\sqrt {s(s - a)(s - b)(s - c)}$ where a, b, and c are the sides of the triangle and 's' is the semi-perimeter; s = (a + b + c)/2.

What is the Formula to Calculate the Area of a Triangle?

The formula for the area of a triangle depends on the dimensions that are known and also on the type of the triangle. There are different formulas for different types of triangles given above on this page in detail. A few of them are listed below.

AREA OF TRIANGLE WORD PROBLEMS

Problem 1 :

Each triangular face of the Pyramid of Peace in Kazakhstan is made up of 25 smaller equilateral triangles. These triangles have measurements as shown in the diagram. What is the area of one of the smaller equilateral triangles ?

Area of smaller equilateral triangle is

= (1/2) x b x h

Substitute 2 for b and 10.4 for h.

Amy needs to order a shade for a triangular-shaped window that has a base of 6 feet and a height of 4 feet. What is the area of the shade ?

Since the shade is in the shape of triangle, we have to use the formula for area of triangle to find the area of the shade.

Area of the shade is

Substitute 6 for b and 4 for h.

= (1/2) x 6 x 4

= 12 square feet

Example 3 :

Monica has a triangular piece of fabric. The height of the triangle is 15 inches and the triangle’s base is 6 inches. Monica says that the area of the fabric is 90 square inches . What error did Monica make ? Explain your answer.

Area of the triangle is

Substitute 6 for b and 15 for h.

= (1/2) x 6 x 15

= 15 x 3

= 45 square inches

Actual area of the triangular piece of fabric is 45 square inches. But Monica says that area of the fabric is 90 square inches. Which means, she forgot to multiply the product of base and height by 1/2. This is the error that she has made.

Example 4 :

The sixth-grade art students are making a mosaic using tiles in the shape of right triangle. The two sides that meet to form a right angle are 3 centimeters and 5 centimeters long. If there are 200 tiles in the mosaic, what is the area of the mosaic ?

Area of each tile is

Substitute 5 for b and 3 for h.

= (1/2) x 5 x 3

= 7.5 cm ²

Area of 200 of the mosaic is

= 200 x 7.5

= 1500 cm ²

Example 5 :

Wayne is going to paint the side of the house shown in the diagram. What is the area that will be painted? Explain how you found your answer.

Wayne's house in the above picture is made up of using two shapes. One is triangle and and other one is rectangle.

By finding the sum of areas of triangle and rectangle, we can get the required area that will be painted.

Required area is

= Area of triangle + Area of rectangle

= [(1/2 ) x b x h] + [l x w]

= [(1/2) x 25 x 8] + (25 x 12)

= 100 + 300

= 400 square ft

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AREA OF TRIANGLE WORD PROBLEMS · = (1/2) x b x h · Substitute 2 for b and 10.4 for h. · Substitute 6 for b and 4 for h. · Substitute 6 for b and 15 for h.
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