Question

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

A.
16 cm2
B.
18 cm2
C.
20 cm2
D.
36 cm2

Answer 1

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)

Answer 2

Correct choice is D

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=(15)/(20)=(3)/(4).`

Therefore,

`(A_(small))/(A_(large))=\left((3)/(4)\right)^2=(9)/(16)`

and

`A_(small)=(9)/(16)\cdot A_(large)=(9)/(16)\cdot 64=9\cdot 4=36\ cm^2.`