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Area of a Triangle
(KS3, Year 7)

homegeometryfinding the area of a triangle
The area of a triangle is found using the formula:

area triangle 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:

triangle bh

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? triangle

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 cm2
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 cm2.

"Find the Area" Widget

Here is a widget to help you learn the formulas to find the areas of different shapes.
  • Click on the shape you're learning about.
  • Click on the pad to start.
  • Follow the instructions in the bottom-left corner.
  • On the last click, the formula, workings, and answer will appear in the yellow box.
  • Enjoy!
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Lesson Slides

The slider below shows another real example of how to find the area of a triangle.

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:

area of a triangle trigonometry 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:

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?

triangle right rectangle bh What about this triangle below?

triangle rectangle bh
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This page was written by Stephen Clarke.

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