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## Pre-Algebra : Area of a Triangle

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

## Example Question #2 : Area Of A Triangle

## Example Question #3 : 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,

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

## Example Question #4 : Area Of A Triangle

What is the area of this shape?

What is the area of the triangle?

Area of a triangle can be determined using the equation:

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

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:

The right-hand side simplifies to:

Now our equation can be rewritten as:

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

## Example Question #7 : Area Of A Triangle

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

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.

The area of triangle is found using the formula

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

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

## Example Question #10 : Area Of A Triangle

## Report an issue with this question

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## Free Mathematics Tutorials

Area of triangles problems with 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

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

## Solutions to the Above Problems

## More References and Links

## Popular Pages

## Area of Triangle

## What is the Area of a Triangle?

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

Area of a Triangle, A = 1/2 × b × h

## 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.

## Area of a Right Angled Triangle

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

Area of triangle ACB = 1/2 × a × b

## Area of an Equilateral Triangle

## Area of an Isosceles Triangle

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

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

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;

## Related Articles

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.

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

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

## Frequently Asked Questions on Area of a Triangle

## How to find the area of a triangle using vectors?

## How to calculate the area of a triangle?

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

Visit BYJU’S for all Maths related queries and study materials

## 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?

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

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.)

## Leave a Comment Cancel reply

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## Unit 8: Lesson 2

## Area of triangles

- Triangle missing side example
- Your answer should be
- an integer, like 6 6 6 6
- an exact decimal, like 0.75 0.75 0 . 7 5 0, point, 75
- a simplified proper fraction, like 3 / 5 3/5 3 / 5 3, slash, 5
- a simplified improper fraction, like 7 / 4 7/4 7 / 4 7, slash, 4
- a mixed number, like 1 3 / 4 1\ 3/4 1 3 / 4 1, space, 3, slash, 4

## Word Problems - Area of Triangles

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

Area of a Triangle - Algebra and Geometry Help

Algebra and Triangles : solving equations linked to perimeter and area

Find area of a triangle- word problem

Word problem involving area of triangle

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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?

## Derivation of the Area of a Triangle from Rectangle

What is the area of the triangle pictured below?

## 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?

Calculate the area of the triangle pictured below.

What is the area of the following triangle?

## Ultimate Math Solver (Free) Free Algebra Solver ... type anything in there!

Popular pages @ mathwarehouse.com.

## 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

(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?

Area = ½ bh = ½ × 20 × 12 = 120

## Knowing Three Sides

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

## Knowing Two Sides and the Included Angle

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

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.

## How to Remember

Just think "abc": Area = ½ a b sin C

## How Does it Work?

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

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

## 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

## What is the Area of a Triangle?

## Triangle Definition

## Area of Triangle Formula

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

## Area of Triangle Using Heron's Formula

- Step 1: Find the semi perimeter (half perimeter) of the given triangle by adding all three sides and dividing it by 2.
- Step 2: Apply the value of the semi-perimeter of the triangle in the main formula called 'Heron’s Formula'.

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

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

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

= 12 × 1/2 (since sin 30º = 1/2)

## How to Find the Area of a Triangle?

## Area of Triangle Formulas

## Area of a Right-Angled Triangle

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

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

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

- Area of Rectangle
- Area of square
- Area of Circle
- Perimeter of Triangle
- Difference Between Area and Perimeter

## 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

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.

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

go to slide go to slide go to slide

## Practice Questions on Area of Triangle

## What is the Area of Triangle Formula?

- Area of a scalene triangle = \(\sqrt {s(s - a)(s - b)(s - c)}\); where a, b, and c are the sides and 's' is the semi-perimeter; s = (a + b + c)/2
- Area of triangle = 1/2 × side 1 × side 2 × sin(θ); when 2 sides and the included angle is known, where θ is the angle between the given two sides.
- Area of an equilateral triangle = (√3)/4 × side 2
- Area of an isosceles triangle = 1/4 × b\(\sqrt {4{a^2} - {b^2}}\); where 'b' is the base and 'a' is the length of an equal side.

## How to Find the Base and Height of a Triangle?

## How to Find the Area and Perimeter of a Triangle?

## How to Find the Area of a Triangle Without Height?

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

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

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

## AREA OF TRIANGLE WORD PROBLEMS

Area of smaller equilateral triangle is

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.

Substitute 5 for b and 3 for h.

= Area of triangle + Area of rectangle

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

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