Question

The figure above shows a big square that contains 2 smaller squares in orange and four half circles in red. If the side of the big containing square is 9 inches long, what is the total area of orange?A. 40.16 in2B. 41.62 in2C. 42.53 in2D. 43.49 in2

Answer 1

To solve this question we will use the following diagram:

Therefore:

$\begin{gathered} 2r_1+r_1=9in, \\ 2r_2+r_2=2r_{1.} \end{gathered}$

Adding like terms in the above equations we get:

$\begin{gathered} 3r_1=9in, \\ 3r_2=2r_1\text{.} \end{gathered}$

Therefore:

$\begin{gathered} r_1=\frac{9in}{3}=3in, \\ r_2=\frac{6in}{3}=2in\text{.} \end{gathered}$

Now, notice that the orange region is formed by 2 semicircles of radius 3in and 2 semicircles of radius 1in, then, the area is:

$\begin{gathered} A=\pi(3in)^2+\pi(2in)^2 \\ =9\pi in^2+4\pi in^2 \\ =13\pi in^2\approx40.84in^2. \end{gathered}$

Answer: 40.84in².