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 the side - lengths

The ratio of the side - lengths of the two similar figures is $\frac{9}{12}=\frac{3}{4}$.

Step2: Recall the relationship between the ratio of side - lengths and the ratio of areas

For two similar figures, if the ratio of their side - lengths is $a:b$, the ratio of their areas is $a^{2}:b^{2}$. So the ratio of the areas of the two similar figures is $(\frac{3}{4})^{2}=\frac{9}{16}$.

Step3: Set up a proportion to find the unknown area

Let the unknown area be $A$. We know that $\frac{A}{32}=\frac{9}{16}$. Cross - multiply gives $16A = 32\times9$.

Step4: Solve for the unknown area

$16A=288$, then $A=\frac{288}{16}=18$.

Answer:

$18$