Question

The polygons are similar. The area of one polygon is given. Find the area of the other polygon.3 ft6 ftA = 27 ft?Area =ft?

Answer 1

Let be "A" the area of the other polygon (in square feet).

By definition, when two figures are similar, the ratio of the lengths corresponding sides can be written as following:

`(a)/(b)`

And the ratio of the areas of two similar figures can be expressed as:

`(a^2)/(b^2)`

Then, the ratio of the areas can be calculated by squaring the ratio of their corresponding sides.

In this case, you can identify that:

`\begin{gathered} a=6ft \\ b=3ft \end{gathered}`

Then, the ratio of the areas is:

`k_{\text{areas}=}((6ft)^2)/((3ft)^2)=4`

Then:

`\begin{gathered} A=(4)(27ft^2) \\ A=108ft^2 \end{gathered}`

The answer is:

`108ft^2`