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

`(10)/(8)=(5)/(4)`

Then,

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

Thus, the answer is 64in^2