Functional Skills: Area

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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 and compound shapes.

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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}

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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}

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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}

FS Level 1FS Level 2AQAEdexcelCity & GuildsNCFEOpen AwardsHighfield Qualifications
FS Level 1AQAEdexcelCity & GuildsNCFEOpen AwardsHighfield Qualifications
FS Level 2AQAEdexcelCity & GuildsNCFEOpen AwardsHighfield Qualifications

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

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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

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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

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Functional Skills: Area Example Questions

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

Area of a rectangle = width \times length

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

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

Additional Resources

PFS

Exam Tips Cheat Sheet

FS Level 2
PFS

Formula Booklet

FS Level 2

Functional Skills: Area Worksheet and Example Questions

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