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Understand Shapes With the Same Area but Different Perimeter

In this worksheet, students will be asked to use their knowledge of how to calculate the area and perimeter of shapes. They will have an understanding that shapes with the same area can have different perimeters and vice versa. This worksheet will involve problem solving using these concepts.

'Understand Shapes With the Same Area but Different Perimeter' worksheet

Key stage:  KS 2

Curriculum topic:   Measurement

Curriculum subtopic:   Calculate Areas

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.

Shapes with the same area can have different perimeters.

 

You will need to use this knowledge to solve a series of questions and solve some problems.

Can you complete the blank spaces to show the area and perimeter of the blue shape?

 

           
           
           
           
           
           

Can you complete the blank spaces to show the perimeter of Shapes 1 and 2?

 

Shape 1

           
           
           
           
           
           

 

Shape 2

           
           
           
           
           
           

 

Shape 1 and 2 do not have the same area or same perimeter...true or false?

 

Shape 1

           
           
           
           
           
           

 

Shape 2

           
           
           
           
           
           

 

True

False

What is the perimeter and area of this shape? 

 

           
           
           
           
           
           
Perimeter = 10cm Area = 6cm²

Perimeter = 10cm Area = 10cm²

Perimeter = 10cm Area = 8cm²

Perimeter = 10cm Area = 6cm²

What is the area and perimeter of this shape?

 

 
           
           
           
           
           
           
Area = 4cm² Perimeter = 10cm

Area = 3cm² Perimeter = 10cm

Area = 5cm² Perimeter = 10cm

Area = 4cm² Perimeter = 11cm

What do these 2 shapes have in common?

 

           
           
           
           
           
           

 

           
           
           
           
           
           

What is the difference in area between these 2 shapes?

 

           
           
           
           
           
           

 

           
           
           
           
           
           
2 cm

20 cm²

4 cm²

2 cm²

What is the area and perimeter of this shape?

 

           
           
           
           
           
           
2 cm

20 cm²

4 cm²

2 cm²

What is the area and perimeter of this shape?

 

           
           
           
           
           
           
2 cm

20 cm²

4 cm²

2 cm²

Which statement is correct about these two shapes?

 

           
           
           
           
           
           

 

 

           
           
           
           
           
           

 

Both shapes have the same perimeter

Both shapes have the same area and perimeter

Both shapes have the same area

The shapes have nothing in common

  • Question 1

Can you complete the blank spaces to show the area and perimeter of the blue shape?

 

           
           
           
           
           
           
CORRECT ANSWER
EDDIE SAYS
Remember to find the area, count the number of squares. To find the perimeter, add the total of the distances around all of the sides. Area = 12 cm² Perimeter = 16 cm
  • Question 2

Can you complete the blank spaces to show the perimeter of Shapes 1 and 2?

 

Shape 1

           
           
           
           
           
           

 

Shape 2

           
           
           
           
           
           

 

CORRECT ANSWER
EDDIE SAYS
The perimeter is the total distance of all of the sides added together. Shape 1 has a perimeter of 20cm. Shape 2 has a perimeter of 14cm.
  • Question 3

Shape 1 and 2 do not have the same area or same perimeter...true or false?

 

Shape 1

           
           
           
           
           
           

 

Shape 2

           
           
           
           
           
           

 

CORRECT ANSWER
False
EDDIE SAYS
False! Although Shape 1 and 2 have different perimeters, they do in fact have the same area of 12cm². Remember, in order to find the area, count the squares.
  • Question 4

What is the perimeter and area of this shape? 

 

           
           
           
           
           
           
CORRECT ANSWER
Perimeter = 10cm Area = 6cm²
EDDIE SAYS
This time, the perimeter was 10cm and the area was 6cm².
  • Question 5

What is the area and perimeter of this shape?

 

 
           
           
           
           
           
           
CORRECT ANSWER
Area = 4cm² Perimeter = 10cm
EDDIE SAYS
The measurements for this shape are: Perimeter = 10cm Area = 4cm²
  • Question 6

What do these 2 shapes have in common?

 

           
           
           
           
           
           

 

           
           
           
           
           
           
CORRECT ANSWER
EDDIE SAYS
The red and blue shape have one feature in common and that is the perimeter. Both shapes have a perimeter of 10cm.
  • Question 7

What is the difference in area between these 2 shapes?

 

           
           
           
           
           
           

 

           
           
           
           
           
           
CORRECT ANSWER
2 cm²
EDDIE SAYS
The red and blue shapes have different areas to one another despite having the same perimeter. The red shape has an area of 6 cm² and the blue shape an area of 4 cm², leaving a difference of 2 cm². Is this getting easier? You're almost at the end of the activity, keep focusing!
  • Question 8

What is the area and perimeter of this shape?

 

           
           
           
           
           
           
CORRECT ANSWER
EDDIE SAYS
How did you get on? The area of the shape is the number of squares and is 8 cm². The perimeter of the shape is the total distance around the shape and is 14 cm.
  • Question 9

What is the area and perimeter of this shape?

 

           
           
           
           
           
           
CORRECT ANSWER
EDDIE SAYS
How did you find this question? The area of the shape is the number of squares and is 8 cm². The perimeter of the shape is the total distance around the shape and is 18 cm.
  • Question 10

Which statement is correct about these two shapes?

 

           
           
           
           
           
           

 

 

           
           
           
           
           
           

 

CORRECT ANSWER
Both shapes have the same area
EDDIE SAYS
Remember to read each statement carefully. The shapes both have the same area of 8 cm². Great focus, that's the activity finished! How about taking a well deserved rest and trying another?
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