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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

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 class=

Respuesta :

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)

frika

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 [tex]k^2.[/tex]

You are given corresponding lengths in two similar figures, then

[tex]k=\dfrac{15}{20}=\dfrac{3}{4}.[/tex]

Therefore,

[tex]\dfrac{A_{small}}{A_{large}}=\left(\dfrac{3}{4}\right)^2=\dfrac{9}{16}[/tex]

and

[tex]A_{small}=\dfrac{9}{16}\cdot A_{large}=\dfrac{9}{16}\cdot 64=9\cdot 4=36\ cm^2.[/tex]

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