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Calculate Areas: Triangles

In this worksheet, students must calculate the areas of the given triangles.

'Calculate Areas: Triangles' worksheet

Key stage:  KS 2

Curriculum topic:   Measurement

Curriculum subtopic:   Calculate Areas

Difficulty level:  

Worksheet Overview

Use the following formula to work out the area of a rectangle:

Rectangle area

 

We must know:

  • the base length
  • the perpendicular height from the base to the top.

 

Area of rectangle = base × height

 

 

Now, try this with a piece of paper.

Start with a rectangle.

Rectangle

 

Cut off a right-angled triangle from the left-hand side and separate the two pieces.

The area of the two pieces together will be the same as the original rectangle.

Cut right-angled triangle from left-hand side of rectangle

 

Cut off a right-angled triangle from the right-hand side to form a triangle in the middle, and separate the three pieces.

The area of the three pieces will still be the same as the original rectangle.

Cut right-angled triangle from the middle of paper

 

Now look carefully at the pieces marked A and B below.

Notice that the areas match. 

A matches A and B matches B.

Matching triangles from rectangle

 

So the area of the triangle in the middle is half the area of the rectangle.

 

 

Area of Triangles

Area of triangle

We must know:

  • the base length
  • the perpendicular height from the base to the apex. (NOT the slant heights)

 

Area of triangle = ½ base × height

or

Area of triangle = base × height ÷ 2

 

 

Example

Calculate the area of this triangle in cm2.

Area of triangle

 

Answer

This is a triangle.

We must know:

  • the base length
  • the perpendicular height from the base to the top. (NOT the slant height)

 

If we turn our heads to the left, the base length is 12 cm and the perpendicular height is 6 cm.

We do not need to know the slant height of 10 cm to use the formula.

 

Now we use the area formula:

Area of triangle = ½ base × height

Area = ½ × 12 × 6 = 6 × 6  =  36 cm2

 

Or...

 

Area of triangle = base × height ÷ 2

Area = 12 × 6  ÷ 2 = 72 ÷ 2 =  36 cm2

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