Edexcel IGCSE Math A 4.11 Similarity Question Bank

Practise using scale factors in similar shapes, from missing lengths and scale drawings to area and volume ratio problems.

Exam points

use linear scale factors from diagrams or maps to find lengths and real distances
convert linear scale factors to area or volume scale factors for similar solids
work backwards from surface area or volume information to find a missing value

Covered syllabus points

4.11.A Geometrical properties of similar figures 4.11.B Maps and scale drawings 4.11.HA Area scale factors 4.11.HB Volume scale factors 4.11.HC Areas and volumes of similar figures

[Maximum number: 4]

4 A B C and DEF are similar triangles.

Figure for Question 4.11 Similarity question 1 — Edexcel IGCSE Math A Higher

Diagram NOT accurately drawn

(a)

Work out the length of DE. cm

The area of triangle DEF is $525 \mathrm{~cm}^{2}$

[ 2 ]

$40\div16\times12=30$

Final answer:
30

(b)

Find the area of triangle DEF in $\mathrm{m}^{2}$ $\mathrm{m}^{2}$

[ 2 ]

$525\div100^2=0.0525$

Final answer:
0.0525

Accept:
$5.25\times10^{-2}$

[Maximum number: 1]

The scale drawing shows the position of a hall and the position of a library.

Figure for Question 4.11 Similarity question 2 — Edexcel IGCSE Math A Higher

Scale: 1 cm represents 20 metres

A post box is 140 metres from the library on a bearing of $220^{\circ}$

Use your scale drawing to find

the real distance, in metres, of the hall from the post box,

Accept:
$150\text{ m} \text{ to } 158\text{ m}$

B1.

[Maximum number: 4]

17 A and B are two similar vases.

Figure for Question 4.11 Similarity question 3 — Edexcel IGCSE Math A Higher

Diagram NOT accurately drawn

Vase A has height 24 cm.
Vase B has height 36 cm.
Vase A has a surface area of $960 \mathrm{~cm}^{2}$

(a)

Work out the surface area of vase B.

Vase B has a volume of $V \mathrm{~cm}^{3}$

[ 2 ]

eg $\frac{24}{36}$ or 2: 3 oe or $\frac{36}{24}$ or 3: 2 oe

M1 for a correct scale factor

2160

A1

(b)

Find in terms of V, an expression for the volume, in $\mathrm{cm}^{3}$ , of vase A.
$\mathrm{cm}^{3}$

[ 2 ]

$\left(\frac{24}{36}\right)^3$
or
$2^3:3^3$
oe, or reciprocal equivalents.

Final answer:
$\frac{8}{27}V$
oe, e.g.
$\frac{V}{3.375}$

Marking guidance:
- M1 for correct scale factor for volume, ft from linear scale factor in part (a) or ft from $\sqrt{2160/960}$
- A1 for $\frac{8}{27}V$ oe

All question bank results loaded

Covered syllabus points

4.11 Similarity question 1

Question (a)

Question (b)

4.11 Similarity question 2

4.11 Similarity question 3

Question (a)

Question (b)