Question

Find the area of the shaded region in the figure. Use the pi key for pi.The area of the shaded region in the figure is approximately: ft or ft^2(Type an integer or decimal rounded to the nearest tenth as needed.)

Answer 1

The area of the shaded region is equal to the area of the circle minus the area of the square, let's rember the formula to calculate the area of these figures:

`\begin{gathered} A_(\bigcirc)=\frac{\pi d^{2^{}}}{4} \\ \\ A_(\square)=l^2 \end{gathered}`

Remember that d is the diameter and l is the square length, then, let's apply these formulas:

`\begin{gathered} A_T=A_(\bigcirc)-A_(\square) \\ \\ A_T=(\pi d^2)/(4)-l^2 \end{gathered}`

The diameter is 3.1 ft and the length is 2.5 ft, then

`\begin{gathered} A_T=(\pi(3.1)^2)/(4)-(2.5)^2 \\ \\ A_T=1.3\text{ ft}^2 \end{gathered}`

Therefore, the area of the shaded region is 1.3 ft^2.