How_To_Be_Good_At_Math

MEASUREMENT • COMPARING AREA AND PERIMETER 177

What’s happened to the

area and the perimeter?

When we changed the shape,

we removed 10 cm^2 from the

bottom, but replaced it with

only 3 cm^2 on the side.

So, the perimeter has stayed

the same, but the area is

now smaller.

The area of the crocodile enclosure

is 400 m². This is greater than the

leopard enclosure, even though they both

have the same perimeter.

So, we can see that shapes with the

same perimeter don’t always have

the same area.

Take a look at this rectangle.

If we keep the perimeter the

same, but make it 1 cm longer and

take 1 cm off the width, you might

think the area would stay the same.

If we multiply the lengths of the sides

of the leopard enclosure, we can see

that its area is 375 m².

10 cm

11 cm

4 cm

3 cm

10 cm^2

removed

3 cm^2

added

Perimeter = 28 cm

Area = 40 cm^2 Perimeter = 28 cm Area = 33 cm 2

Same perimeter but

different area

Now look at these two enclosures. They

both have a perimeter of 80 m. Does this

mean that they have the same area too?

Why aren’t they

the same?

When we change the

measurements of a shape,

why don’t the perimeter

and area change by the

same amount? Perimeter

is a measure of the length

around the edge of a

shape. Area is a measure

The volumes of solids

by the perimeter. This

means that when we

change one, the other isn’t

affected in the same way.

20 m

15 m

20 m

25 m

Perimeter = 80 m

Area = 400 m²

Perimeter = 80 m

Area = 375 m²

176_177_Comparing_area_and_perimeter.indd 177 29/02/2016 18:03