Question

1.4 i can find the area of similar figures. find the value of the area of the larger figure given that they are similar. be sure to include units in your answer. if necessary, round your answer to the nearest tenth. write proportion here. area: 54 inches squared area: __ 6 in 15 yd

Explanation:

Step1: Find the ratio of side - lengths

The ratio of the side - lengths of the two similar hexagons is $\frac{15}{6}=\frac{5}{2}$.

Step2: Use the ratio of areas formula

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 smaller hexagon be $A_1 = 54$ square inches and the area of the larger hexagon be $A_2$. The ratio of the side - lengths is $\frac{5}{2}$, so the ratio of the areas is $(\frac{5}{2})^2=\frac{25}{4}$. We can set up the proportion $\frac{A_2}{A_1}=\frac{25}{4}$.

Step3: Solve for the area of the larger hexagon

Substitute $A_1 = 54$ into the proportion $\frac{A_2}{54}=\frac{25}{4}$. Cross - multiply to get $4A_2=54\times25$. Then $4A_2 = 1350$. Divide both sides by 4: $A_2=\frac{1350}{4}=337.5$ square inches.

Answer:

$337.5$ square inches