Maths topic

area and perimeter

Area and perimeter are two different measurements. Area counts the space inside a shape. Perimeter measures the distance around the outside.

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the big idea

Area and perimeter can be measured on the same shape, but they answer different questions. Area asks how much flat space is covered. Perimeter asks how far it is around the boundary.

area inside space
perimeter around the outside
units units or square units

change the rectangle

Choose a rectangle and compare its area with its perimeter.

12 square units, 14 units around

3 by 4 rectangle

areaarea = 12 square units perimeterperimeter = 14 units remember12 inside squares, 14 units around the outside.
rectangle

perimeter goes around

Perimeter is the distance around the outside edge of a shape.

  • Trace the boundary around the outside.
  • Add the side lengths to find the perimeter.
  • A 3 by 4 rectangle has perimeter 3 + 4 + 3 + 4 = 14 units.
14 units around
3 + 4 + 3 + 4 = 14 units

area covers the inside

Area is the amount of flat space inside a shape.

  • Count the square units that cover the inside.
  • A 3 by 4 rectangle covers 12 square units.
  • Area is written with square units.
12 square units inside
3 rows x 4 = 12 square units

same shape, two measurements

The same rectangle has an area and a perimeter. They measure different things.

  • The inside squares show the area.
  • The outside edge shows the perimeter.
  • Do not swap the answers: 12 square units is area, 14 units is perimeter.
12 square units, 14 units around
insidearea = 12 square units outsideperimeter = 14 units

units tell what was measured

Perimeter uses length units. Area uses square units because it measures covered space.

  • Perimeter might be 14 units, 14 cm or 14 m.
  • Area might be 12 square units or 12 square centimetres.
  • The word square is a clue that the measurement is area.
perimeter 14 units distance around
area 12 square units space covered

same area can have different perimeter

Two shapes can cover the same number of square units but have different distances around the outside.

  • A 3 by 4 rectangle has area 12 square units and perimeter 14 units.
  • A 2 by 6 rectangle also has area 12 square units, but perimeter 16 units.
  • Same area does not always mean same perimeter.
12 square units, 14 units around
3 x 4 area = 12 square units perimeter = 14 units
12 square units, 16 units around
2 x 6 area = 12 square units perimeter = 16 units

Both have area 12 square units. The perimeter is different.

same perimeter can have different area

Two shapes can have the same distance around the outside but cover different inside spaces.

  • A 3 by 5 rectangle has perimeter 16 units and area 15 square units.
  • A 4 by 4 square also has perimeter 16 units, but area 16 square units.
  • Same perimeter does not always mean same area.
15 square units, 16 units around
3 x 5 area = 15 square units perimeter = 16 units
16 square units, 16 units around
4 x 4 area = 16 square units perimeter = 16 units

Both have perimeter 16 units. The area is different.

measurement words

These words help us tell area and perimeter apart.

1 area inside

how much flat space is covered

2 perimeter around

the distance around the outside edge

3 unit length

used for perimeter, such as cm or m

4 square unit area

used for area because squares cover the inside

5 side length edge

one length around the shape

6 rectangle rows and columns

area can be counted as rows of square units

area and perimeter facts

fact Perimeter goes around the outside
fact Area covers the inside
3 by 4 area 12 square units
3 by 4 perimeter 14 units
fact Same area can have different perimeter
fact Same perimeter can have different area

real world examples

fencing perimeter helps work out how much fence is needed
garden beds perimeter follows the outside edge
carpet area helps work out how much floor is covered
painting area helps estimate how much wall space is painted
tiling area counts how many square tiles fit
room plans area and perimeter help compare spaces

quick area and perimeter quiz

Try a few ideas. This quiz only asks about ideas shown on this page.

Which measurement covers the inside of a shape?

Which measurement goes around the outside edge?

A 3 by 4 rectangle covers how many square units?

A 3 by 4 rectangle has perimeter 3 + 4 + 3 + 4. What is it?

If two rectangles have the same area, must they have the same perimeter?