Question

a rectangular paper - board measuring 35 in long and 28 in wide has a semi - circle cut out of it, as shown below. find the area of the paperboard that remains. use the value 3.14 for π, and do not round your answer. be sure to include the correct unit in your answer.

Explanation:

Step1: Calculate area of rectangle

The area formula for a rectangle is $A = l\times w$, where $l = 35$ in and $w = 28$ in. So, $A_{rectangle}=35\times28 = 980$ in².

Step2: Calculate area of semi - circle

The diameter of the semi - circle is equal to the width of the rectangle, so $d = 28$ in and the radius $r=\frac{d}{2}=\frac{28}{2}=14$ in. The area formula for a semi - circle is $A=\frac{1}{2}\pi r^{2}$. Substituting $\pi = 3.14$ and $r = 14$ in, we get $A_{semicircle}=\frac{1}{2}\times3.14\times14^{2}=\frac{1}{2}\times3.14\times196 = 307.72$ in².

Step3: Calculate remaining area

The remaining area $A_{remaining}=A_{rectangle}-A_{semicircle}$. So, $A_{remaining}=980 - 307.72=672.28$ in².

Answer:

$672.28$ in²