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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:  Maths and Numerical Reasoning

Curriculum subtopic:  2D Shapes: Triangles, Quadrilaterals and Polygons

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

You should already know the following formula to work out the area of a rectangle:

 

You 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.

 

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 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.

 

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

Notice that the areas match. 

A matches A and B matches B.

 

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

 

 

Area of Triangles

You 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.

 

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

Select the correct formula to calculate the area of a triangle.

area = base × perpendicular height

area = ½ base × perpendicular height

area = base × slant height

Calculate the area of this triangle in cm2.

(Just write the number.)

 

Calculate the area of this triangle in cm2.

(Just write the number.)

 

Calculate the area of this triangle in cm2.

(Just write the number.)

 

Calculate the area of this right-angled triangle in cm2.

(Just write the number.)

 

Calculate the area of this triangle in cm2.

(Just write the number.)

Which of these two triangles has the larger area?

The base lengths and the perpendicular heights are shown.

 

A

B

cannot tell

Which of these two triangles has the larger area?

The base lengths and the perpendicular heights are shown.

A

B

cannot tell

Which of these two triangles has the larger area?

 

A

B

cannot tell

Is this statement true or false?

"These triangles have the same area."

true

false

cannot tell

  • Question 1

Select the correct formula to calculate the area of a triangle.

CORRECT ANSWER
area = ½ base × perpendicular height
EDDIE SAYS
This is the same as base × height ÷ 2.
  • Question 2

Calculate the area of this triangle in cm2.

(Just write the number.)

 

CORRECT ANSWER
40
EDDIE SAYS
Base length = 10 cm
Perpendicular height = 8 cm
Area = 10 × 8 ÷ 2 = 80 ÷ 2 = 40 cm2
  • Question 3

Calculate the area of this triangle in cm2.

(Just write the number.)

 

CORRECT ANSWER
42
EDDIE SAYS
Base length = 12 cm
Perpendicular height = 7 cm
Area = ½ × 12 × 7 = 6 × 7 = 42 cm2
  • Question 4

Calculate the area of this triangle in cm2.

(Just write the number.)

 

CORRECT ANSWER
35
EDDIE SAYS
Base length = 14 cm
Perpendicular height = 5 cm
Area = ½ × 14 × 5 = 7 × 5 = 35 cm2
  • Question 5

Calculate the area of this right-angled triangle in cm2.

(Just write the number.)

 

CORRECT ANSWER
60
EDDIE SAYS
Base length = 15 cm
Perpendicular height = 8 cm
Area = 15 × 8 ÷ 2 = 15 × 4 = 60 cm2
  • Question 6

Calculate the area of this triangle in cm2.

(Just write the number.)

CORRECT ANSWER
54
EDDIE SAYS
Base length = 12 cm
Perpendicular height = 9 cm
Area = 12 × 9 ÷ 2 = 108 ÷ 2 = 54 cm2
  • Question 7

Which of these two triangles has the larger area?

The base lengths and the perpendicular heights are shown.

 

CORRECT ANSWER
A
EDDIE SAYS
Same base lengths, but the height of A is more.
So the area of A will be bigger.
  • Question 8

Which of these two triangles has the larger area?

The base lengths and the perpendicular heights are shown.

CORRECT ANSWER
B
EDDIE SAYS
Area of A = 12 × 10 ÷ 2 = 60 cm2
Area of B = 16 × 8 ÷ 2 = 64 cm2
  • Question 9

Which of these two triangles has the larger area?

 

CORRECT ANSWER
cannot tell
EDDIE SAYS
Area of B = 5 × 7 = 35 cm2
We cannot work out the area of A because the perpendicular height is not shown.
  • Question 10

Is this statement true or false?

"These triangles have the same area."

CORRECT ANSWER
true
EDDIE SAYS
Area of top triangle = 10 × 8 ÷ 2 = 40 cm2
Area of bottom triangle = 16 × 5 ÷ 2 = 40 cm2
---- OR ----

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