 # Same Area - Different Perimeter

In this worksheet, students must recognise that shapes with the same areas can have different perimeters. Key stage:  KS 2

Curriculum topic:  Maths and Numerical Reasoning

Curriculum subtopic:  Perimeter and Area

Difficulty level:   ### 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.

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.

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.

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 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.)

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.)

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.)

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.)

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.)

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.)

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.)

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.)

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.)

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."

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

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