Question

these figures are similar. the area of one is given. find the area of the other. area = 32 in² 9 in 12 in ? in²

Explanation:

Step1: Find the ratio of side lengths

The ratio of side lengths is $\frac{9}{12}=\frac{3}{4}$.

Step2: Use the ratio of areas formula

For similar figures, if the ratio of side lengths is $a:b$, the ratio of areas is $a^{2}:b^{2}$. Here, the ratio of areas is $(\frac{3}{4})^{2}=\frac{9}{16}$. Let the area of the smaller figure be $A$. We know the area of the larger figure is $32\ in^{2}$. So $\frac{A}{32}=\frac{9}{16}$.

Step3: Solve for $A$

Cross - multiply: $16A = 9\times32$. Then $A=\frac{9\times32}{16}$. Simplify: $A = 18$.

Answer:

$18$