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 □ ft²
(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 $A_{circle}=\pi r^{2}$. Given the diameter of the circle is $2.9$, the radius $r = \frac{2.9}{2}=1.45$. So $A_{circle}=\pi\times(1.45)^{2}=\pi\times2.1025$.

Step2: Find area of the square

The formula for the area of a square is $A_{square}=s^{2}$, where $s = 1.2$. So $A_{square}=(1.2)^{2}=1.44$.

Step3: Find area of the shaded region

The area of the shaded region $A = A_{circle}-A_{square}=\pi\times2.1025 - 1.44$. Using $\pi\approx3.14$, we have $A\approx3.14\times2.1025-1.44=6.60185 - 1.44 = 5.16185\approx5.2$.

Answer:

$5.2$