Exploring measures
Area of rectangles and triangles
Area is the amount of surface a shape covers, measured in square units. In this section we work out the area of rectangles by multiplying, and the area of triangles by seeing them as half of a rectangle.
Area of a rectangle
The area of a rectangle = length × width. A square is a special rectangle, so its area = side × side. Area is measured in square units: mm², cm², m² and km².
Area of a triangle
If you cut a rectangle in half along its diagonal, you get two equal triangles. So the area of the triangle is half the area of the rectangle. Work out the rectangle's area, then divide by 2.
Working backwards
If you already know a triangle's area, the rectangle it was cut from has double that area. So multiply the triangle's area by 2.
Estimating by counting squares
On centimetre squared paper, each square is 1 cm². Count the whole squares a triangle covers, then add a half for each square that is only half covered. Two half squares make one whole square.
Worked examples
Area of a rectangle
- The rectangle is 8 m long and 4 m wide.
- Area of a rectangle = length × width.
- Multiply: 8 × 4.
Answer: The area is 32 m².
Area of a triangle from a rectangle
- The rectangle 8 m by 4 m has an area of 8 × 4 = 32 m².
- The triangle is half of the rectangle.
- Divide the rectangle's area in half: 32 ÷ 2.
Answer: Each triangle has an area of 16 m².
Finding the rectangle from a triangle
- A triangle has an area of 9 cm².
- It is half of a rectangle, so the rectangle is double the triangle.
- Multiply: 9 × 2.
Answer: The rectangle has an area of 18 cm².
Estimating a triangle's area by counting squares
- Each square on the grid is 1 cm².
- Count the whole squares the triangle covers: 6.
- 4 half squares make 2 more whole squares, so add 2.
Answer: The triangle's area is about 8 cm².
Working out how many bags of seed
- A field 10 m by 8 m has an area of 10 × 8 = 80 m².
- One 1 kg bag of grass seed covers 20 m².
- Divide: 80 ÷ 20.
Answer: You need 4 bags.
Where you see this in real life
- Working out how many bags of grass seed to buy to cover a field.
- Covering triangular biscuits with icing.
- Tiling a rectangular floor.
- Working out how much paper is needed to wrap a shape.
Key words
- Area
- The amount of surface a shape covers, measured in square units.
- Rectangle
- A four-sided shape with four right angles and opposite sides equal.
- Square
- A special rectangle with all four sides equal.
- Triangle
- A three-sided shape; half of a rectangle when the rectangle is cut along its diagonal.
- Square centimetre (cm²)
- The area of a square that is 1 cm by 1 cm.