Question

find the area of the figure below, composed of a rectangle and a semicircle. the circle is shown. round to the nearest tenths place. 14 3 answer attempt 1 out of 2

Explanation:

Step1: Calculate rectangle area

The length of the rectangle is 14 and the width is 6 (diameter of the semi - circle, $d = 2r=6$). The area formula for a rectangle is $A_{rect}=l\times w$. So $A_{rect}=14\times6 = 84$.

Step2: Calculate semi - circle area

The area formula for a circle is $A=\pi r^{2}$, and for a semi - circle $A_{semicircle}=\frac{1}{2}\pi r^{2}$. Given $r = 3$, then $A_{semicircle}=\frac{1}{2}\times\pi\times3^{2}=\frac{9\pi}{2}\approx\frac{9\times3.14}{2}=14.13$.

Step3: Calculate total area

The total area of the figure $A = A_{rect}+A_{semicircle}$. So $A=84 + 14.13=98.13\approx98.1$.

Answer:

98.1