Area and perimeter
The perimeter is the distance around a shape: we add all the sides and answer in a unit of length, for example cm. The area is the surface inside: for a rectangle base · height, for a triangle base · height ÷ 2. The area is given in a unit of area, for example cm².
Watch Fox work it out on the board
Fox works one step at a time. Press play.
Perimeter or area?
| Perimeter | Area | |
|---|---|---|
| What it is | The distance around the shape | The surface inside the shape |
| How we calculate | Add all the sides | Multiply, for example base · height |
| Unit | cm, m, km | cm², m², km² |
| Everyday example | A fence around a garden | A carpet in a room |
1 cm² is a square that is 1 cm long and 1 cm wide. The area counts how many of these squares fit inside.
Rectangle and square
A rectangle of 7 cm · 4 cm holds 4 rows of 7 squares.
Area = b · h = 7 · 4 = 28 cm²
Perimeter = 7 + 4 + 7 + 4 = 22 cm
A square with side 6 cm has an area of 6 · 6 = 36 cm² and a perimeter of 4 · 6 = 24 cm.
Area formulas for more shapes
The height is always at right angles to the base. It is not the same as a slanting side.
| Shape | Area | Why |
|---|---|---|
| Rectangle | b · h | h rows with b squares in each. |
| Square | s · s | A rectangle with sides of equal length. |
| Parallelogram | b · h | Move a triangle from one end to the other, and it becomes a rectangle. |
| Triangle | b · h ÷ 2 | Two identical triangles make a parallelogram. |
| Trapezium | (a + b) · h ÷ 2 | Two identical trapeziums, one turned round, make a parallelogram with base a + b. |
In the trapezium, a and b are the two parallel sides. The perimeter is always the sum of all the sides. The height only counts in the perimeter when it is also a side.
Example
Example 1: the floor of a room, 5 m by 3 m
We want to know how much carpet (area) and skirting board (perimeter) the room needs.
The area: the floor is a rectangle, so we calculate base · height.
A = 5 · 3 = 15 m²
The unit is m², because we count squares of 1 m · 1 m.
A = 15 m²
The perimeter: two walls are 5 m and two are 3 m.
O = 5 + 3 + 5 + 3 = 16 m
The room needs 15 m² of carpet and 16 m of skirting board.
3 rows of 5 squares is 5 + 5 + 5 = 15. The perimeter is also 2 · 5 + 2 · 3 = 16 m.
Example 2: a triangle with base 10 cm and height 6 cm
We want to find the area. Two identical triangles make a parallelogram, so we calculate base · height ÷ 2.
We multiply the base by the height.
10 · 6 = 60
The triangle is half of that, so we divide by two.
60 ÷ 2 = 30
The area of the triangle is 30 cm².
A = 30 cm²
A rectangle of 10 cm · 6 cm has an area of 60 cm². The triangle covers exactly half, so 30 cm² is reasonable.
Pitfalls
Calculating 7 · 4 when the question is about the distance around the rectangle.
Around means perimeter: add the sides. Surface means area: multiply.
Using a slanting side instead of the height.
The height is at right angles to the base. A slanting side is longer and gives an area that is too large.
Writing the wrong unit, for example an area of 28 cm or a perimeter of 22 cm².
Area has a unit with ²: cm², m². Perimeter is a distance: cm, m.
Practise on your own
0 of 4 correct1A square has sides of 7 cm. What is the perimeter?
2A rectangle is 9 cm long and 6 cm wide. What is the area?
3A triangle has base 14 cm and height 5 cm. What is the area?
4A trapezium has parallel sides of 6 cm and 10 cm. The height is 7 cm. What is the area?
More walkthroughs with Fox
Common questions
Can two shapes have the same perimeter but different areas?
Yes. A rectangle of 5 cm · 1 cm and a square of 3 cm · 3 cm both have a perimeter of 12 cm. The areas are 5 cm² and 9 cm².
How do you find the area of a compound shape, for example an L-shaped room?
Split the shape into rectangles and triangles. Work out each part and add the areas.
How many cm² are there in one m²?
1 m² is a square with side 100 cm. It holds 100 · 100 = 10 000 cm².
Read also
- Years 6–9Area and circumference of a circleHow do you work out the area and circumference of a circle?
- Years 4–9Converting unitsHow do you convert units?
- Years 5–9Volume of a cuboid, prism and cylinderHow do you work out volume?
- Years 8–9 and upper secondaryPythagoras' theorem step by stepWhat does Pythagoras' theorem say and how do you use it?
- Years 5–9Scale: maps, drawings and enlargementsHow do you calculate with scale?
Keep practising with Somokai
Free to start. Hints and explanations when you get stuck.
Start practising for freeFound a mistake? Get in touch