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Alika [10]
3 years ago
15

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

Mathematics
2 answers:
nikitadnepr [17]3 years ago
7 0

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.

butalik [34]3 years ago
5 0

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)

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