Question

The diagram shows corresponding lengths in two similar figures. Find the area of the smaller figure.

Answer 1

Answer:

Correct choice is D

Step-by-step explanation:

If two similar figures have the coefficient of similarity k, then the ratio between the area of these figures is equal to $k^2.$

You are given corresponding lengths in two similar figures, then

$k=\dfrac{15}{20}=\dfrac{3}{4}.$

Therefore,

$\dfrac{A_{small}}{A_{large}}=\left(\dfrac{3}{4}\right)^2=\dfrac{9}{16}$

and

$A_{small}=\dfrac{9}{16}\cdot A_{large}=\dfrac{9}{16}\cdot 64=9\cdot 4=36\ cm^2.$

Answer 2

The area are in the ratio of the squares of corresponding sides.

That is  15^2 : 20^2  = 225:400

so the area of the smaller figure = (225/400) * 64

= 0.5625 * 64

= 36 cm^2  (answer)