Functional Skills: Area

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

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}

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}