what is the area of the shaded portion of the circle? (5π - 11.9) ft² (5π - 5.8) ft² (25π - 11.9) ft² (25π…

Explanation:

Step1: Calculate the area of the sector

The formula for the area of a sector of a circle is $A_{sector}=\frac{\theta}{360^{\circ}}\times\pi r^{2}$, where $\theta = 72^{\circ}$ and $r = 5$ ft. $A_{sector}=\frac{72^{\circ}}{360^{\circ}}\times\pi\times5^{2}=\frac{1}{5}\times25\pi = 5\pi$ square - feet.

Step2: Calculate the area of the triangle

The formula for the area of a triangle is $A_{triangle}=\frac{1}{2}bh$. Here, the base $b = 2.9+2.9 = 5.8$ ft and the height $h = 4.1$ ft. $A_{triangle}=\frac{1}{2}\times5.8\times4.1=11.99\approx11.9$ square - feet.

Step3: Calculate the area of the shaded region

The area of the shaded region $A$ is the area of the sector minus the area of the triangle. $A=(5\pi - 11.9)$ square - feet.

Answer:

$(5\pi - 11.9)\text{ ft}^2$