# Functional Skills: Area

## Functional Skills: Area Revision

**Area**

The **area** of 2D shape is the amount of surface it occupies.

Area is calculated by multiplying lengths together, so the metric units for area are **squared **– cm^2, m^2, mm^2 etc. For imperial units for area, we usually say square inches (sq. in) instead of in^2, for example.

You will need to know **4** skills to calculate the area of a **square**, a **rectangle**, a **triangle**Â and **compound shapes**.

**Skill 1: Area of a Square**

The formula for the area of a **square **is:

\text{Area} =a \times a = a^2

where a is the **length **of the sides of the square.

Written in words, this is:

\text{Area} = \text{length} \times \text{length} = \text{length}^2

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**Skill 2: Area of a Rectangle**

The formula for the area of a rectangle is:

\text{Area} = a\times b

where a is the **width **of the rectangle and b is the **length**.

Written in words, this is:

\text{Area} = \text{width} \times \text{length}

**Skill 3: Area of a Triangle**

The formula for the area of a **triangle** is:

\text{Area} = \dfrac{1}{2}\times b \times h

where b is the base **width **of the triangle and h is the vertical **height **as shown in the diagram on the right.

Written in words, this is:

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

**Skill 4: Area of Compound Shapes**

Sometimes, you may need to split up a compound shape into easier shapes to find the area.

**Example:** Find the area of the shape to the right.

For this shape you could either:

- Split the shape up into two rectangles, calculate the area of each rectangle and add them up.
- Notice that the shape is a large rectangle, with a smaller rectangle cut out of it. So, we could calculate the area of the smaller rectangle and minus it from the larger rectangle. This would be easier in this situation:

\text{Area of larger rectangle} = 7 \times 12.5 = \textcolor{red}{87.5 \text{ m}^2}

\text{Area of smaller rectangle} = 5 \times 10 = \textcolor{blue}{50 \text{ m}^2}

\text{Area of shape} = \textcolor{red}{87.5} - \textcolor{blue}{50} = \textcolor{limegreen}{37.5 \text{ m}^2}

**Example 1: Area of a Square**

Calculate the area of a square with sides of length 6 \text{ cm}.

**[1 mark]**

\text{Area of square} = 6 \times 6 = 6^2 = 36 \text{ cm}^2

**Example 2: Area of a Rectangle**

Calculate the area of the rectangle shown to the right.

**[2 marks]**

\text{Area of rectangle} = 12 \times 5 = 60 \text{ cm}^2

**Example 3: Area of a Triangle**

Calculate the area of the triangle shown to the right.

**[2 marks]**

\text{Area of triangle} = \dfrac{1}{2} \times 9 \times 6 = 27 \text{ cm}^2

## Functional Skills: Area Example Questions

**Question 1:Â **Calculate the area of the triangle ABC shown below, which has a base of 9.8 cm and a height of 11.2 cm.

**[2 marks]**

Using the formula for the area of a triangle:

Area = \dfrac{1}{2}\times base \times height

Area = \dfrac{1}{2}\times 9.8 \times 11.2=54.88 cm^2

**Question 2: **Calculate the area of the rectangle shown below.

**[1 mark]**

Area of a rectangle = width \times length

Area = 5.1\times7.6=38.76 cm^2

**Question 3: **Below is a right-angled triangle on top of a square. Using the measurements given, calculate the area of the whole shape.

**[3 marks]**

Area of the Square = 6.3\times 6.3=39.69 cm^2

To work out the area of the triangle we need to know the height. This can be found by subtracting the side length of the square from the total height of the shape: 10.5-6.3=4.2 cm

Area of the triangle = \dfrac{1}{2}\times6.3\times4.2=13.23 cm^2

Total area = 39.69 + 13.23 = 52.92 cm^2

## Functional Skills: Area Worksheet and Example Questions

### Area L1

FS Level 1NewOfficial PFS### Area L2

FS Level 2NewOfficial PFS[responsive-flipbook id=”pfs_pocket_revision_guide_-_sample”]

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