Question

find the area of the shaded region in the figure. use the π key for π. the area of the shaded region in the figure is approximately □ ft. (type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Find area of the circle

The formula for the area of a circle is $A_{circle}=\pi r^{2}$, where the diameter of the circle is $d = 4.2$, so the radius $r=\frac{4.2}{2}=2.1$. Then $A_{circle}=\pi\times(2.1)^{2}=4.41\pi$.

Step2: Find area of the square

The formula for the area of a square is $A_{square}=s^{2}$, where the side - length of the square $s = 1.5$. So $A_{square}=(1.5)^{2}=2.25$.

Step3: Find area of the shaded region

The area of the shaded region $A = A_{circle}-A_{square}=4.41\pi - 2.25$.
Using $\pi\approx3.14$, we have $A=4.41\times3.14 - 2.25=13.8474-2.25 = 11.5974\approx11.6$.

Answer:

$11.6$