year 8 maths

8F
Similar figures
499
11 a If a regular polygon, such as this regular octagon, is enlarged, do the interior angles change?
b Are all polygons with the same number of sides similar? Give reasons.
12 If a square is similar to another by a scale factor of 4 , what is the ratio of the area of small square
to the area of large square?
ENRICHMENT
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13
Square designs
13 A square design consists of a series of squares, as shown. An inner square is formed by joining the
midpoints of the sides of the next largest square.
4 cm
a
Use Pythagoras’ theorem to find the side length of:
i the second largest square
ii the third largest square
b Find the scale factor of a pair of consecutive squares; for example, first and second or second
and third.
c
If the side length of the outside square is x cm , show that the scale factor of consecutive squares
is equal to the result found in part b .
d What is the scale factor of a pair of alternate squares; for example, first and third or second
and fourth?
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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