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Same Area - Different Perimeter

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

'Same Area - Different Perimeter' worksheet

Key stage:  KS 2

Curriculum topic:  Measurement

Curriculum subtopic:  Recognise Shapes

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

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

 

           
           
           
           
           
           


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

 

The 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.

 

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

 

           
           
           
           
           
           


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

 

The 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 2 + 1 + 1 + 1 + 1 + 1 + 2 + 1 + 1 + 1 + 1 + 1 = 14 cm.

 

Shapes with the same area can have different perimeters.

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

 

           
           
           
           
           
           

 

What is its area in cm2?

(Just write the number.)

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

 

           
           
           
           
           
           

 

What is its perimeter in cm?

(Just write the number.)

Here is another shape, drawn on a centimetre square grid.

It also has an area of 8 cm2.

 

           
           
           
           
           
           

 

What is its perimeter in cm?

(Just write the number.)

Here is another shape, drawn on a centimetre square grid.

It also has an area of 8 cm2.

 

           
           
           
           
           
           

 

What is its perimeter in cm?

(Just write the number.)

Here is another shape, drawn on a centimetre square grid.

It also has an area of 8 cm2.

 

           
           
           
           
           
           

 

What is its perimeter in cm?

(Just write the number.)

Look at the 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.)

Here is another shape, drawn on a centimetre square grid.

It also has an area of 12 cm2.

 

           
           
           
           
           
           

 

What is its perimeter in cm?

(Just write the number.)

Here is another shape, drawn on a centimetre square grid.

It also has an area of 12 cm2.

 

           
           
           
           
           
           

 

What is its perimeter in cm?

(Just write the number.)

Is this statement true or false?

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

true

false

  • Question 1

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

 

           
           
           
           
           
           

 

What is its area in cm2?

(Just write the number.)

CORRECT ANSWER
8
EDDIE SAYS
4 × 2 = 8 cm2
  • Question 2

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

 

           
           
           
           
           
           

 

What is its perimeter in cm?

(Just write the number.)

CORRECT ANSWER
12
EDDIE SAYS
4 + 2 + 4 + 2 = 12 cm
  • Question 3

Here is another shape, drawn on a centimetre square grid.

It also has an area of 8 cm2.

 

           
           
           
           
           
           

 

What is its perimeter in cm?

(Just write the number.)

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

Here is another shape, drawn on a centimetre square grid.

It also has an area of 8 cm2.

 

           
           
           
           
           
           

 

What is its perimeter in cm?

(Just write the number.)

CORRECT ANSWER
18
EDDIE SAYS
1 + 3 + 3 + 2 + 1 + 3 + 3 + 2 = 18 cm
  • Question 5

Here is another shape, drawn on a centimetre square grid.

It also has an area of 8 cm2.

 

           
           
           
           
           
           

 

What is its perimeter in cm?

(Just write the number.)

CORRECT ANSWER
18
EDDIE SAYS
1 + 3 + 2 + 1 + 5 + 1 + 2 + 3 = 18 cm
  • Question 6

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

 

           
           
           
           
           
           

 

What is its area in cm2?

(Just write the number.)

CORRECT ANSWER
12
EDDIE SAYS
Count the 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
16
EDDIE SAYS
2 + 2 + 2 + 2 + 4 + 4 = 16 cm
  • Question 8

Here is another shape, drawn on a centimetre square grid.

It also has an area of 12 cm2.

 

           
           
           
           
           
           

 

What is its perimeter in cm?

(Just write the number.)

CORRECT ANSWER
14
EDDIE SAYS
4 + 3 + 4 + 3 = 14 cm
  • Question 9

Here is another shape, drawn on a centimetre square grid.

It also has an area of 12 cm2.

 

           
           
           
           
           
           

 

What is its perimeter in cm?

(Just write the number.)

CORRECT ANSWER
20
EDDIE SAYS
2 + 2 + 2 + 1 + 2 + 1 + 4 + 3 + 2 + 1 = 20 cm
  • Question 10

Is this statement true or false?

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

CORRECT ANSWER
false
EDDIE SAYS
This worksheet shows that this is false.
---- OR ----

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