Area
Area is the amount of space taken up by a surface or a 2D shape. It is measured in squares with metric units mm², cm², m² and km².
Calculating areas
The area can be calculated by counting squares.
Example
Calculate the area of this shape if each square is 1 cm².
There are 10 squares inside the shape so the area is 10 cm².
Calculating areas of rectangles
The area of rectangles can be calculated by multiplying the length by the width.
Example
Calculate the area of this rectangle.
Example
Calculate the width of a rectangle with an area of 40 mm² and a length of 8 mm.
Work backwards to find the width:
Area = length x width
40 = 8 x width
width = 40 ÷ 8 (opposite of x is ÷)
= 5 mm
Question
Calculate the area of a square of side 12 m.
Length = 12 m
Width = 12 m
Area = length x width
Area = 12 x 12 = 144 m²
Calculating areas of triangles
A triangle can be formed by drawing a diagonal across a rectangle and splitting the shape along that line. The area of the triangle will be exactly half of the area of the rectangle.
The area of triangles can be calculated by multiplying the length (or base) by the height and dividing by 2.
This is written as a formula.
\(\text{Area of triangle} = \frac{\text{base} \times \text{height}}{2}\)
Or
\(\text{Area of triangle} = \frac{1}{2}bh\)
The formula works for all triangles provided the perpendicular height is used.
Example
Calculate the area of a triangle with a base of 4.2 cm and a height of 7.5 cm.
\(\text{Area of triangle} = \frac{\text{base} \times \text{height}}{2}\)
Area = 4.2 x 7.5 ÷ 2 = 15.75 cm²
Example
Calculate the area of a triangle with a base of 9 cm and a perpendicular height of 6 cm.
\(\text{Area of triangle} = \frac{\text{base} \times \text{height}}{2}\)
Area = 9 x 6 ÷ 2 = 27 cm²
Question
Calculate the area of the triangle.
\(\text{Area of triangle} = \frac{\text{base} \times \text{height}}{2}\)
Area = 5 x 5 ÷ 2 = 12.5 m²
Area = 12.5 m²
Calculating a missing length given the area
To find a missing length it is necessary to work backwards when the area and only one of the dimensions are known.
Example
Calculate the height of a triangle with a base of 4.8 cm and an area of 7.2 cm².
Base x Height ÷ 2 = Area
Work backwards:
Area x 2 ÷ Base = Height
7.2 x 2 ÷ 4.8
14.4 ÷ 4.8 = 3
Height = 3 cm
Question
The area of the triangle is 21 cm². Calculate the base when the height is 6 cm.
Base x Height ÷ 2 = Area
Work backwards:
Area x 2 ÷ Height = Base
21 x 2 ÷ 6 = Base
42 ÷ 6 = Base
Base = 7 cm
Area of compound shapes
Compound shapes are shapes that can be split into 2 or more shapes.
To calculate the area of compound shapes:
- Split the shape into easier shapes
- Calculate the area of each part
- Add the areas to get the total
Example
Calculate the area of this shape.
Split the shape into easier shapes
Calculate the area of each part
A = 4 x 12 = 48
B = 4 x 8 = 32
C = 8 x 12 = 96
- Add the areas to get the total
48 + 32 + 96 = 176 cm²
Question
Calculate the area of the arrow.
Split the shape into easier shapes
Calculate the area of each part
Base x Height ÷ 2 = Area
36 x 15 ÷ 2 = 270
30 x 16 = 480
- Add the areas to get the total
270 + 480 = 750 cm²
Area = 750 cm²
Test yourself
More on M1: Geometry and measures
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