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Pentagons R and S are similar. The area of pentagon R is [tex]13 \, \text{cm}^2[/tex]. Calculate the area of pentagon S.

Answer :

The area of pentagon S is 52 square cm.

It is given that the pentagons R and S are similar and that the area of R is 13 cm². We are asked to calculate the area of pentagon S.

Since the two pentagons are similar, we know that the ratio of their areas is equal to the square of the ratio of their side lengths. Let the side length of R be $r$ and the side length of S be $s$ We are given that the area of R is $13 cm^2$ , so we can set up the following proportion to find the ratio of the side lengths:

[tex]$\dfrac{13}{A_s} = \left(\dfrac{r}{s}\right)^2$[/tex]

We are also given that one of the side lengths of R is 7 cm and another side length of S is 14 cm. We can set up another proportion to find the ratio of the side lengths: [tex]$\dfrac{7}{14} = \dfrac{r}{s}$[/tex]

Solving for [tex]$\dfrac{r}{s}$[/tex] in the second proportion, we get [tex]$\dfrac{r}{s} = \dfrac{1}{2}$[/tex] . Substituting this into our first proportion, we get:

[tex]$\dfrac{13}{A_s} = \left(\dfrac{1}{2}\right)^2$[/tex]

Simplifying the right side of this equation, we get [tex]$\dfrac{13}{A_s} = \dfrac{1}{4}$[/tex] . Multiplying both sides by [tex]$A_s$[/tex] , we get [tex]$13 = \dfrac{A_s}{4}$[/tex] . Multiplying both sides by 4, we get [tex]$A_s = 52$[/tex] square cm.

The complete question is: Pentagons R and S are similar. The area of pentagon R is 13cm squared Calculate the area of s

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