Question

These figures are similar. The area of one is given. Find the area of the other.3 inarea=24 in6 in[ ? Jin2

Answer 1

ANSWER

$\begin{equation*} 6\text{ }in^2 \end{equation*}$

EXPLANATION

We want to find the area of the other figure.

Since the figures are similar, the areas of the figures are related by the square of the linear scale factor.

To find the linear scale factor, we have to divide a corresponding set of side lengths from the two figures. That is:

$\begin{gathered} \frac{3}{6} \\ \Rightarrow\frac{1}{2} \end{gathered}$

Hence, the areas of the figures have a scale factor of:

$\begin{gathered} (\frac{1}{2})^2 \\ \Rightarrow\frac{1}{4} \end{gathered}$

So, to find the area of the other figure, we have to multiply the area of the figure by 1/4:

$\begin{gathered} 24*\frac{1}{4} \\ \Rightarrow6\text{ }in^2 \end{gathered}$

That is the area of the other figure.