Edexcel IGCSE Math B 6.G similarity

Practise similarity questions by finding the linear scale factor, then squaring or cubing it for area or volume quantities.

Exam points

Use squared scale factors for surface areas of mathematically similar solids.
Use cubed scale factors to calculate or compare volumes of similar shapes.
Find missing lengths, areas or volumes after matching corresponding dimensions.

[Maximum number: 3]

Figure 1 shows triangle OAB in which $\overrightarrow{O A}=4 \mathbf{a}$ and $\overrightarrow{O B}=8 \mathbf{b}$
P is the point on OA such that O P: O A=1: 4

The area of APQB is 150 cm².

Calculate the area of triangle OPQ.

Triangles OAB and OPQ are similar.
$|\triangle OAB|=4^{2}|\triangle OPQ|$

The area of APQB is:
$150=|\triangle OAB|-|\triangle OPQ|$ $150=4^{2}|\triangle OPQ|-|\triangle OPQ|$ $150=15|\triangle OPQ|$ $|\triangle OPQ|=10$

Final answer:
$10\text{ cm}^{2}$

M1: similar-triangle area scale factor.
M1 (dep): using the difference of the two triangle areas for APQB.
A1.

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6.G Similarity question 1