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Compound Shapes in GCSE Maths

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Compound Shapes – Introduction

Compound shapes are geometric figures that consist of two or more simpler shapes combined together. In GCSE Maths, understanding compound shapes is crucial for calculating their area, perimeter, and other related measurements

Calculating the Area:
 To find the area of a compound shape, you need to break it down into simpler shapes and calculate their individual areas. Then, sum up the areas of all the component shapes to get the total area of the compound shape.

Calculating the Perimeter:
 Similar to finding the area, calculating the perimeter of a compound shape requires breaking it down into its constituent shapes. Once you have the individual perimeters, add them together to obtain the total perimeter of the compound shape.

Identifying Component Shapes:
 When dealing with compound shapes, it’s important to identify the simpler shapes that make up the compound shape. These may include rectangles, triangles, circles, trapeziums, and semi-circles. Recognizing these component shapes enables you to calculate their measurements accurately.

Applying Formulas:
 To calculate the area and perimeter of individual shapes within a compound shape, you’ll need to apply the appropriate formulas. For example, the area of a rectangle is calculated by multiplying its length by its width, while the area of a triangle is found using the formula: 0.5 * base * height.

Compound Shapes - Examples 1 to 3

\begin{aligned} 5 \times 7 & =35 \\ 1 / 2 \times 4 \times 5 & =10 \end{aligned}

Total area = 45 \mathrm{~cm}^2

\begin{aligned} 8 \times 9 & =72 \\ \frac{1}{2} \times 12 \times 5 & =30 \end{aligned}

Total area = 102 \mathrm{~cm}^2

\begin{aligned} 5 \times 6 & =30 \\ 1 / 2 \times 4 \times 5 & =10 \end{aligned}

Total area = 40 \mathrm{~cm}^2

Compound Shapes - Examples 4 to 6

\begin{aligned} & 3 \times 4=12 \\ & 1 \times 2=2 \end{aligned}

Total area = 10 m^2

\begin{aligned} 2 \times 12 & =24 \\ \frac{1}{2} \times 6 \times 5 & =15 \end{aligned}

Total area = 39 \mathrm{~cm}^2

\begin{aligned} & 10 \times 8=80 \\ & 4 \times 2=8 \\ & 80-(3 \times 8) \\ & 80-24=56 \mathrm{~cm}^2 \end{aligned}
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Compound Shapes – Examples 7 to 9

 
\begin{aligned} 12 \times 5 & =60 \\ 1 / 2 \times 4 \times 5 & =10 \end{aligned}
Total area = 70 \mathrm{~cm}^2
 
\begin{aligned} 1 / 2 \times 12 \times 10 & =60 \\ 3 \times 5 & =15 \end{aligned}\begin{aligned}
1 / 2 \times 12 \times 10 & =60 \\
3 \times 5 & =15
\end{aligned}
Total area = 45 \mathrm{~cm}^2
 
 
 
\begin{aligned} 75 \times 100 & =7500 \\ \frac{1}{2} \times 70 \times 85 & =\frac{2975}{10475} \end{aligned}
 
Total money = 10475 \times 3=31,425
 

Conclusion:
 In GCSE Maths, compound shapes are complex figures formed by combining simpler shapes. To calculate the area and perimeter of a compound shape, break it down into its constituent shapes, calculate their individual measurements, and then sum them up. Understanding compound shapes and applying the relevant formulas are essential skills for solving geometry problems in GCSE Maths.

When it comes to doing questions with compound shapes you can split the shape in any suitable direction that you see fit. 

Doing this might mean you will see some different values but the overall answer should match. 

If you, or your parents would like to find out more, please just get in touch via email at info@exam.tips or call us on 0800 689 1272. 

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