Question

the figures below are similar. the labeled sides are corresponding. what is the area of the smaller triangle?

Answer 1

When we have similar figures, its lengths have a constant ratio. In this case, the ratio from the smallest to the biggest is:

`r=(8)/(9)`

The areas of similar figures are related to the square of the ratio of the lengths, that is:

`\begin{gathered} r^2=\frac{A_{\text{smallest}}}{A_{\text{biggest}}}=(A_2)/(A_1) \\ A_2=r^2A_1=((8)/(9))^2\cdot81ft^2=(64)/(81)\cdot81ft^2=64ft^2 \end{gathered}`

So, the area of the smllest triangle is 64ft².