Question

1. find the area of the shaded parts of the following figure. round your answer to the nearest tenth. 25 in. 18 in.

Explanation:

Step1: Calculate rectangle area

The area formula for a rectangle is $A = l\times w$. Here, $l = 25$ in and $w = 18$ in, so $A_{rectangle}=25\times18 = 450$ in².

Step2: Calculate semi - circle area

The diameter of the semi - circle is 18 in, so the radius $r=\frac{18}{2}=9$ in. The area formula for a full - circle is $A=\pi r^{2}$, and for a semi - circle $A_{semicircle}=\frac{1}{2}\pi r^{2}$. Substituting $r = 9$ in, we get $A_{semicircle}=\frac{1}{2}\pi\times9^{2}=\frac{1}{2}\pi\times81 = 40.5\pi$ in².

Step3: Calculate shaded area

The shaded area $A_{shaded}=A_{rectangle}-A_{semicircle}$. Substitute the values: $A_{shaded}=450 - 40.5\pi$. Using $\pi\approx3.14$, we have $A_{shaded}=450-40.5\times3.14=450 - 127.17=322.83\approx322.8$ in².

Answer:

$322.8$ in²