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Same Perimeter - Different Area

In this worksheet, students must recognise that shapes with the same perimeters can have different areas.

'Same Perimeter - Different Area' worksheet

Key stage:  KS 2

Curriculum topic:  Maths and Numerical Reasoning

Curriculum subtopic:  Perimeter and Area

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

Look at the red shape below, drawn on a centimetre square grid:

 

           
           
           
           
           
           

 

Its perimeter is the total of the distances around all four sides.

Starting at the base and going anticlockwise around the shape, we work out that:

the perimeter is 2 + 3 + 2 + 3 = 10 cm.

 

It is made of 6 centimetre squares, so its area is 6 cm2.

 

Now look at the blue shape below, drawn on a centimetre square grid:

 

           
           
           
           
           
           



Its perimeter is the total of the distances around all its sides.

Starting at the base and going anticlockwise around the shape, we work out that:

the perimeter is 1 + 1 + 1 + 2 + 1 + 1 + 1 + 2 = 10 cm.

This is the same perimeter as the red shape above.

 

But it is only made of 4 centimetre squares, so its area is only 4 cm2.

 

Shapes with the same perimeter can have different areas.

Look at the blue shape below, drawn on a centimetre square grid:

 

           
           
           
           
           
           

 

What is its perimeter in cm?

(Just write the number.)

Look at the same blue shape below, drawn on a centimetre square grid:

 

           
           
           
           
           
           

 

What is its area in cm2?

(Just write the number.)

Look at the blue shape below, drawn on a centimetre square grid:

 

           
           
           
           
           
           

 

What is its perimeter in cm?

(Just write the number.)

Look at the same blue shape below, drawn on a centimetre square grid:

 

           
           
           
           
           
           

 

What is its area in cm2?

(Just write the number.)

Look at the blue shape below, drawn on a centimetre square grid:

 

           
           
           
           
           
           

 

What is its perimeter in cm?

(Just write the number.)

Look at the same blue shape below, drawn on a centimetre square grid:

 

           
           
           
           
           
           

 

What is its area in cm2?

(Just write the number.)

Look at the blue shape below, drawn on a centimetre square grid:

 

           
           
           
           
           
           

 

What is its perimeter in cm?

(Just write the number.)

Look at the same blue shape below, drawn on a centimetre square grid:

 

           
           
           
           
           
           

 

What is its area in cm2?

(Just write the number.)

Complete this sentence.

"All the shapes in this worksheet have had the same _________."

area

perimeter

area and perimeter

Is this statement true or false?

"Shapes that have the same perimeter must also have the same area."

true

false

  • Question 1

Look at the blue shape below, drawn on a centimetre square grid:

 

           
           
           
           
           
           

 

What is its perimeter in cm?

(Just write the number.)

CORRECT ANSWER
14
EDDIE SAYS
2 + 2 + 1 + 2 + 3 + 4 = 14 cm
  • Question 2

Look at the same blue shape below, drawn on a centimetre square grid:

 

           
           
           
           
           
           

 

What is its area in cm2?

(Just write the number.)

CORRECT ANSWER
10
EDDIE SAYS
There are 10 squares.
  • Question 3

Look at the blue shape below, drawn on a centimetre square grid:

 

           
           
           
           
           
           

 

What is its perimeter in cm?

(Just write the number.)

CORRECT ANSWER
14
EDDIE SAYS
2 + 2 + 1 + 2 + 2 + 1 + 1 + 3 = 14 cm
  • Question 4

Look at the same blue shape below, drawn on a centimetre square grid:

 

           
           
           
           
           
           

 

What is its area in cm2?

(Just write the number.)

CORRECT ANSWER
9
EDDIE SAYS
There are 9 squares.
  • Question 5

Look at the blue shape below, drawn on a centimetre square grid:

 

           
           
           
           
           
           

 

What is its perimeter in cm?

(Just write the number.)

CORRECT ANSWER
14
EDDIE SAYS
1 + 1 + 1 + 1 + 1 + 2 + 2 + 1 + 1 + 3 = 14 cm
  • Question 6

Look at the same blue shape below, drawn on a centimetre square grid:

 

           
           
           
           
           
           

 

What is its area in cm2?

(Just write the number.)

CORRECT ANSWER
8
EDDIE SAYS
There are 8 squares.
  • Question 7

Look at the blue shape below, drawn on a centimetre square grid:

 

           
           
           
           
           
           

 

What is its perimeter in cm?

(Just write the number.)

CORRECT ANSWER
14
EDDIE SAYS
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 3 = 14 cm
  • Question 8

Look at the same blue shape below, drawn on a centimetre square grid:

 

           
           
           
           
           
           

 

What is its area in cm2?

(Just write the number.)

CORRECT ANSWER
7
EDDIE SAYS
There are 7 squares.
  • Question 9

Complete this sentence.

"All the shapes in this worksheet have had the same _________."

CORRECT ANSWER
perimeter
EDDIE SAYS
They have all had a perimeter of 14 cm.
Their areas have been different.
  • Question 10

Is this statement true or false?

"Shapes that have the same perimeter must also have the same area."

CORRECT ANSWER
false
EDDIE SAYS
This worksheet has shown that shapes with the same perimeter can have different areas.
---- OR ----

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