these figures are similar. the area of one is given. find the area of the other. area = 100 in.² 8 in. 10…

Explanation:

Step1: Find the ratio of side - lengths

The ratio of the side - lengths of the two similar figures is $\frac{8}{10}=\frac{4}{5}$.

Step2: Use the property of the ratio of areas of similar figures

For two similar figures, if the ratio of their side - lengths is $a:b$, the ratio of their areas is $a^{2}:b^{2}$. Here, the ratio of the areas is $(\frac{4}{5})^{2}=\frac{16}{25}$. Let the unknown area be $A$. We know that $\frac{A}{100}=\frac{16}{25}$.

Step3: Solve for the unknown area

Cross - multiply: $25A = 16\times100$. Then $25A=1600$. Divide both sides by 25: $A=\frac{1600}{25}=64$.

Answer:

64 in.$^{2}$