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# Area of a Triangle

(KS3, Year 7)

## The Lesson

The area of a triangle is found using the formula:In this formula,

**b**is the length of the base of the triangle and

**h**is the height of the triangle. The image below shows what we mean by the lengths of the bases and the height:

## How to Find the Area of a Triangle

Finding the area of a triangle is easy.## Question

What is the area of a triangle with a base of 5 cm and a height of 3 cm, as shown below?## Step-by-Step:

# 1

Start with the formula:

Area = ½bh

**Don't forget:**½bh = ½ × b × h# 2

Substitute the length of the base and the height into the formula. In our example, b = 5 and h = 3.

Area = ½ × 5 × 3 = 7.5 cm

^{2}**Don't forget:**½ × a number = 0.5 × a number = a number ÷ 2.## Answer:

The area of the triangle with a base of 5 cm and a height of 3 cm is 7.5 cm^{2}.

## "Find the Area" Widget

## How to Find the Area of a Triangle Using Trigonometry

The area of a triangle can also be found using trigonometry. The area is found using the formula:In the formula,

**a**and

**b**are lengths of two sides of the triangle and

**C**is the angle between them. The image below shows what we mean by the two sides and the angle between them:

Read more about how to find the area of a triangle using trigonometry

## What Is a Triangle?

A triangle is a flat shape with three straight sides and three corners (also called vertices). There are different types of triangle:## What's in a Name?

A triangle has three corners and so three angles. Just as a tricycle has three wheels, and a tripod has three legs, a shape with three angles in called a triangle.## Areas of Triangles and Rectangles

The area of a triangle is ½bh. The area of a rectangle is bh. The area of the triangle is half that of the rectangle with the same base length and height. Can you see from the image of a right-angled triangle below that this is the case?What about this triangle below?

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