these figures are similar. the area of one is given. find the area of the other. area = 196 in.² 15 in. 21…

Explanation:

Step1: Find the ratio of side - lengths

The ratio of the side - lengths of the two similar figures is $\frac{15}{21}=\frac{5}{7}$.

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 $a^{2}:b^{2}$. Let the area of the unknown figure be $A$. Then $\frac{A}{196}=(\frac{5}{7})^{2}$.

Step3: Solve for $A$

We have $\frac{A}{196}=\frac{25}{49}$. Cross - multiply: $49A = 196\times25$. Then $A=\frac{196\times25}{49}$. Since $196\div49 = 4$, $A = 4\times25=100$.

Answer:

$100$ in.$^{2}$