Area

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Measurement Units

Area: The area of a figure is the amount of space inside that shape.
The units of area are square units.(eg. mm², cm²,m²)

We can use the formulae to find the areas of basic shapes.

Shape Area (A)

Square

A = l2
where l is the length of a side.

Rectangle

A = l × w
where l is the length, w is the width

Parallelogram

A = b × h
where b is the base length, h is the height.

Triangle

A = ½ b ×h
where b is the base length, h is the height.

Trapezium

A = ½ (a+b)h
where a and b are the side lengths of the parallel sides, h is the height.

Rhombus

A = ½ a× b
where a and b are the lengths of the diagonals

Kite

A = ½ a× b
where a and b are the lengths of the diagonals

Circle

Area of Composite figures: To find the area of a composite figure, first you split up the composite figure into simpler shapes(eg: shapes like squares, rectangles, triangles, circles etc.) and then find the areas of each of the shapes and add them up.
The units of area are square units.(eg. mm², cm²,m²)

Example

Example 1.
Let's find the area this figure.

To find the area of the figure, we need to add the areas of Fig.(a),Fig.(b) and Fig.(c).
First we need to identify the shapes.
(a) and (b) are rectangles and (c) is a triangle.
Then, we can use the formula to find the area.

Area of a rectangle = length × width

Area of a triangle    = ½ base × height     where base =3, height =2

Area of Fig.(a)   = 6 × 4     = 24

Area of Fig.(b)   = 4 × 2       =    8

Area of Fig.(c)   = ½ × 3 × 2 =   3

Total area          = 24 + 8 + 3 = 35 square units

Example 2.
Find the area of the shaded part

We want to find the area of the shaded part.
First we need to identify the shapes.We have a rectangle and a circle.
Then write down the formulae for areas of these shapes.

Rectangle:

A = l × w where l is the length, where l = 26cm , w = 10cm
w is the width.

Circle:

diameter of the circle = 5 cm, radius = ½ of 5 = 2.5cm

Area of the circle           = 3.142 × 2.5 × 2.5
                                     = 19.6375 cm²
                                     = 19.6 cm²      (rounded off to one decimal place.)

Area of the rectangle = 26 × 10 cm²
= 260 cm²

Area of the shaded part = Area of the rectangle - Area of the circle
                                    = 260 - 19.6
                                    = 240.4 cm²

Have a Go

Problem 1
Find the area of this figure.

          Problem 2
          Find the area of this figure.

Practice Questions

Question 1
Find the area of the triangle.

Question 2
Find the area of the flower bed.

Solution 1

Area of (a) = 10 × 6 = 60
Area of (b) = ½ × 10 × 6 = 30
Area of the figure = 60 + 90
= 150square units

back to Have a Go

To find the area of the figure, first we need to identify the shapes.
Fig.(a)   rectangle
Fig.(b)   triangle
Then we have to use the formula to calculate the area of each shape.

Rectangle:
A = l × w where l is the length,
                  w is the width, A is the area.
where l = 10units ,   w = 6units

Triangle:
A = ½ b ×h where b is the base length,
                     h is the height, A is the area.
where b= 10 units, h= 6 units

Substitute the values and calculate the areas and add them together to find the total area.

Solution 2

Area of (a) =12 × 6 = 72 cm²
Area of (b) = (3.142 × 3 × 3) ÷ 2
= 14.139 cm²
= 14.1 cm² (rounded off to one decimal place.)

Total area = 72 + 14.1 = 86.1 cm²

back to Have a Go

Identify the shapes.
Fig.(a) ~ rectangle
Fig.(b) ~ semicirle
Use the formulae to calculate the areas.
Rectangle:
A = l × w where l is the length,
w is the width, A is the area.

Area of a Circle:

Area of the semi circle = area of the circle ÷ 2

Area of the semi circle = (3.142 × 3 × 3) ÷ 2

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