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In order to access this I need to be confident with:

2D shapes/polygons

RoundingMultiplication and division

Substituting numbers into formulae Converting between metric unitsBIDMAS

This topic is relevant for:

Here we will learn how to work out area.

There are also how to work out area* *worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

**Area **is a measure of how much space there is inside of a 2 dimensional shape. To find the area of a shape we can either count the number of unit squares within the shape or use the appropriate area formula for that shape.

Area is measured in square units e.g. cm^{2}, \; m^{2}, \; mm^{2} .

The table below shows the formulae for calculating area for some of the most common 2 D shapes:

In order to work out area:

**Write down the formula.****Substitute the values into the formula.****Do the calculation.****Write the answer, including the units.**

Get your free how to work out area worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEGet your free how to work out area worksheet of 20+ questions and answers. Includes reasoning and applied questions.

DOWNLOAD FREEWork out the area of the rectangle

**Write down the formula.**

2**Substitute the values into the formula.**

Here the base is 11cm and the height is 4cm.

Area=11 \times 43**Do the calculation.**

4**Write the answer, including the units.**

The measurements are in centimetres so the area will be measured in square centimetres.

Area=44cm^2Work out the area of the parallelogram

**Write down the formula.**

Area= base \times height

**Substitute the values into the formula.**

Here the base is 10m and the height is 6m.

Area=10 \times 6

**Do the calculation.**

Area=10 \times 6

Area=60

**Write the answer, including the units.**

The measurements are in metres so the area will be measured in square metres.

Area=60m^2

Calculate the area of the rhombus

**Write down the formula.**

\text{Area }=\frac{1}{2} \times \text{ width } \times \text{ height}

**Substitute the values into the formula.**

Here the width is 20mm and the height is 8mm.

\text{Area }=\frac{1}{2} \times 20 \times 8

**Do the calculation.**

\begin{aligned}
\text{Area }&=\frac{1}{2} \times 20 \times 8\\\\
\text{Area }&=80
\end{aligned}

**Write the answer, including the units.**

The measurements are in millimetres so the area will be measured in square millimetres.

Area=80mm^2

Find the area of the trapezium

**Write down the formula.**

\text{Area }=\frac{1}{2}(a+b)h

**Substitute the values into the formula.**

In a trapezium, a and b are the parallel sides and h is the height.

Here a=3, \; b=5 and h=4

\text{Area }=\frac{1}{2}(3+5) \times 4

**Do the calculation.**

\begin{aligned}
&\text{Area }=\frac{1}{2}(3+5) \times 4\\\\
&\text{Area }=\frac{1}{2} \times 8 \times 4\\\\
&\text{Area }=16
\end{aligned}

**Write the answer, including the units.**

The measurements are in cm so the area will be measured in cm^2 .

Area=16cm^2

Work out the area of the triangle

**Write down the formula.**

\text{Area }=\frac{1}{2} \times \text{ base } \times \text{ height}

**Substitute the values into the formula.**

Since this is a right triangle, we can see the base of the triangle is 13mm and the height of the triangle is 6mm .

\text{Area }=\frac{1}{2} \times 13 \times 6

**Do the calculation.**

\begin{aligned}
\text{Area }&=\frac{1}{2} \times 13 \times 6\\\\
\text{Area }&=39
\end{aligned}

**Write the answer, including the units.**

The measurements are in mm so the area will be measured in mm^2 .

Area=39mm^2

Work out the area of the circle. Give your answer to 1 decimal place

**Write down the formula.**

\text{Area }=\pi r^{2}

**Substitute the values into the formula.**

Here the radius, r, is 3.5cm .

\text{Area }=\pi \times 3.5^{2}

**Do the calculation.**

\begin{aligned}
\text{Area }&=\pi \times 3.5^{2}\\\\
\text{Area }&=38.48451001
\end{aligned}

**Write the answer, including the units.**

We need to write the answer to one decimal place and include the units.

Area=38.5cm^2

In order to work out area of a compound shape:

**Draw lines to split the shape into two or more smaller shapes. Label the shapes A, B, C, …****Consider each shape individually.****a)****Work out any measurements that you need.****b) Calculate the area using the methods above.****Add or subtract the relevant areas to find the total area.****Write the answer, including the units.**

Work out the area of the following shape

**Draw lines to split the shape into two or more smaller shapes. Label the shapes A, B, C, …**

**Consider each shape individually.**

Shape A

**a) Work out any measurements that you need.**

For a rectangle, we need the height and the base,both of which we are given.

**b) Calculate the area using the methods above.**

\begin{aligned} \text{Area }&=\text{ base }\times \text{ height}\\\\ &=10 \times 6\\\\ &=60\mathrm{cm}^{2} \end{aligned}

Shape B

**a) Work out any measurements that you need.**

For a trapezium, we need a, \; b and h.

**b) Calculate the area using the methods above.**

\begin{aligned}
\text{Area }&=\frac{1}{2}(a+b)h\\\\
&=\frac{1}{2}(5+10) \times 3\\\\
&=22.5\mathrm{cm}^{2}
\end{aligned}

**Add or subtract the relevant areas to find the total area.**

Total area: 60+22.5=82.5

**Write the answer, including the units.**

\text{Area } =82.5cm^2

Work out the shaded area. Give your answer to one decimal place.

**Draw lines to split the shape into two or more smaller shapes. Label the shapes A, B, C, …**

The shape is already clearly split.

**Consider each shape individually.**

Shape A

**a) Work out any measurements that you need.**

For a triangle we need the height and base, which we are given

**b) Calculate the area using the methods above.**

\begin{aligned}
\text{Area }&= \frac{1}{2} \times \text{ base } \times \text{ height}\\\\
&=\frac{1}{2} \times 10 \times 14\\\\
&=70\mathrm{cm}^{2}
\end{aligned}

Shape B

**a) Work out any measurements that you need.**

Here we need the radius of the circle, which is 3.2cm

**b) Calculate the area using the methods above.**

\begin{aligned}
\text{Area }&=\pi \times r^{2}\\\\
&=\pi \times 3.2^{2}\\\\
&=32.16990877\\\\
&=32.17\mathrm{cm}^{2}
\end{aligned}

**Add or subtract the relevant areas to find the total area.**

Shaded area: 70-32.17=37.83

**Write the answer, including the units.**

\text{Area } =37.8cm^2

**Using an incorrect formula**

There are several different formulae for the different shapes – make sure you use the correct one.

**Using the incorrect units/not including units**

Area is measured in square units.

E.g.

Square millimetres, square centimetres, square metres, square inches, square feet, square yards etc.

**Calculating with different units**

All measurements must be in the same units before calculating surface area.

E.g.

You can’t have some measurements in cm and some in m.

**Calculating perimeter/circumference instead of area**

Remember, perimeter is distance around the outside whilst area is the space inside the shape.

**Using diameter instead of radius for a circle**

To work out the area of a circle we need the radius, which is the distance from the centre of the circle to the edge of the circle.

1. Work out the area of the square

14\mathrm{cm}^{2}

49\mathrm{cm}^{2}

28\mathrm{cm}^{2}

42\mathrm{cm}^{2}

Since this is a square, the base and height are the same, 7cm.

\begin{aligned} \text{Area }&=\text{ base } \times \text{ height}\\\\ &=7 \times 7\\\\ &=49\mathrm{cm}^{2} \end{aligned}

2. Work out the area of the parallelogram

55\mathrm{mm}^{2}

18\mathrm{mm}^{2}

36\mathrm{mm}^{2}

77\mathrm{mm}^{2}

The base is 11mm and the height is 5mm.

\begin{aligned} \text{Area }&=\text{ base } \times \text{ height }\\\\ &=11 \times 5\\\\ &=55\mathrm{mm}^{2} \end{aligned}

3. Calculate the area of the rhombus

260\mathrm{m}^{2}

33\mathrm{m}^{2}

16.5\mathrm{m}^{2}

130\mathrm{m}^{2}

\begin{aligned}
\text{Area }&=\frac{1}{2} \times \text{ width } \times \text{ height}\\\\
&=\frac{1}{2} \times 20 \times 13\\\\
&=130\mathrm{m}^{2}
\end{aligned}

4. Find the area of the trapezium

36\mathrm{cm}^{2}

60\mathrm{cm}^{2}

26\mathrm{cm}^{2}

576\mathrm{cm}^{2}

\begin{aligned}
\text{Area }&=\frac{1}{2}(a+b)h\\\\
&=\frac{1}{2} (8+12) \times 6\\\\
&=60\mathrm{cm}^{2}
\end{aligned}

5. Work out the area of the triangle

36\mathrm{mm}^{2}

13\mathrm{mm}^{2}

18\mathrm{mm}^{2}

72\mathrm{mm}^{2}

\begin{aligned}
\text{Area }&=\frac{1}{2} \times \text{ base } \times \text{ height}\\\\
&=\frac{1}{2} \times 9 \times 4\\\\
&=18\mathrm{mm}^{2}
\end{aligned}

6. Calculate the area of the circle. Give your answer to 3sf.

69.1\mathrm{m}^{2}

1520\mathrm{m}^{2}

34.6\mathrm{m}^{2}

380\mathrm{m}^{2}

\begin{aligned}
\text{Area }&=\pi r^{2}\\\\
&=\pi \times 11^{2}\\\\
&=380.132711\\\\
&=380\mathrm{m}^{2}
\end{aligned}

7. Work out the area of the compound shape

418\mathrm{cm}^{2}

550\mathrm{cm}^{2}

561\mathrm{cm}^{2}

286\mathrm{cm}^{2}

Shape A:

\begin{aligned} \text{Area }&=\frac{1}{2} \times \text{ base } \times \text{ height}\\\\ &=\frac{1}{2} \times 22 \times 12\\\\ &=132\mathrm{cm}^{2} \end{aligned}

Shape B:

\begin{aligned} \text{Area }&=\text{ base } \times { height}\\\\ &=22 \times 13\\\\ &=286\mathrm{cm}^{2} \end{aligned}

Total area: 132+286=418cm^2

1. Work out the area of this shape

**(3 marks)**

Show answer

\text{Area of trapezium: }\frac{1}{2}(6+14) \times 8=80\mathrm{cm}^{2}

**(1)**

**(1)**

Total area: 80 + 77 = 157cm^2

**(1)**

2. Sean wants to paint both sides of a fence which is 20m long and 1.5m high.

One tin of the paint that Sean wants to use will cover 15m^2 . How many tins of paint should Sean buy?

**(3 marks)**

Show answer

\text{Area of one side: } 20 \times 1.5 = 30\mathrm{m}^{2}

**(1)**

**(1)**

60 \div 15 = 4 tins

**(1)**

3. A shop sells pizza in two sizes: 10 inches and 13 inches. Would Louise get more pizza if she bought one large pizza or two small pizzas? Show how you decide.

**(3 marks)**

Show answer

\text{Small pizza: Area }=\pi \times 5^{2} = 78.54\text{ square inches}

\text{Two small pizzas: } 2\times 78.54=157.08 \text{ square inches}

**(1)**

\text{Large pizza: Area} = \pi \times 6.5^{2} = 132.72 \text{ square inches}

**(1)**

Two small pizzas

**(1)**

You have now learned how to:

- Work out the area of triangles, quadrilaterals and circles
- Work out the area of compound shapes

- Area of a triangle
- Area of a right angled triangle
- Area of an isosceles triangle
- Area of an equilateral triangle
- Area of a quadrilateral
- Area of a rectangle
- Area of a parallelogram
- Area of a rhombus
- Area of a trapezium
- Area of compound shapes
- Area of a circle
- How to calculate surface area
- How to calculate volume

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