Answered

If the ratio of the corresponding side lengths of two similar polygons is 6:11, what is the ratio of their areas?


A.

6:11

B.

12:11

C.

36:11

D.

36:121

Verified Answer :

hartnn

the ratio of areas is just the square of ratio of sides,
so
(6:11)^2 = 6^2 : 11^2 = 36:121

JeanaShupp

Answer: D. 36:121

Step-by-step explanation:

Given: The ratio of the corresponding side lengths of two similar polygons is

\(r_1:r-2=6:11\\\\\text{OR}\\\\\dfrac{r_1}{r_2}=\dfrac{6}{11}\)

Since we know that the area of any polygon required two dimensions, therefore, the ratio of the surface area of the polygons is given by :-

\(\dfrac{S.A._1}{S.A._2}=\dfrac{r_1^2}{r_2^2}=\dfrac{6^2}{11^2}=\dfrac{36}{121}\)

Hence, the  ratio of their areas= 36:121

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