Question

These figures are similar. The area ofone is given. Find the area of the other.Area = 100 in.28 in.10 in.[? ] in.2

Answer 1

If the dilation coefficient between two figures is equal to k, the ratio between their areas is k^2.

In our case, the dilation coefficient is

$\frac{10}{8}=\frac{5}{4}$

Then,

$\begin{gathered} A_{\text{larger}}=k^2A_{smaller} \\ \Rightarrow A_{\text{smaller}}=\frac{A_{\text{larger}}}{k^2}=\frac{100}{(\frac{5}{4})^2}=\frac{100}{\frac{25}{16}}=16\cdot4=64 \\ \Rightarrow A_{\text{smaller}}=64 \end{gathered}$

Thus, the answer is 64in^2