Question

A circle was inserted into a trapezoid. What is the area of the shaded region? Round your answer to the nearest tenth of a foot. 23 ft ft 10 ft 15 ft a 101.7ft2 202.3ft? x 152 ft? 4.50.3ft2 assessments

Answer 1

We can calculate the shaded area as the area of the trapezoid less the area of the circle.

The area of the trapezoid is:

$\begin{gathered} A_t=\frac{b_1+b_2}{2}\cdot h \\ A_t=\frac{23+15}{2}\cdot8 \\ A_t=\frac{38}{2}\cdot8 \\ A_t=19\cdot8 \\ A_t=152 \end{gathered}$

The area of the circle of radius r=8/2=4 ft is:

$\begin{gathered} A_c=\pi r^2 \\ A_c=\pi\cdot4^2 \\ A_c\approx3.14\cdot16 \\ A_c\approx50.3 \end{gathered}$

Then, the shaded area is the difference between the area of the trapezoid and the area of the circle:

$\begin{gathered} A=A_t-A_c \\ A=152-50.3 \\ A=101.7\text{ ft}^2 \end{gathered}$

Answer: 101.7 ft^2