Question

a figure is composed of a parallelogram and a sector of a circle. what is the area of the figure, to the nearest tenth of a square inch? enter the answer in the box. square inches

Explanation:

Step1: Calculate area of parallelogram

The area formula for a parallelogram is $A = base\times height$. Here, the base is 20 inches and the height is 9 inches. So, $A_{parallelogram}=20\times9 = 180$ square - inches.

Step2: Calculate radius of the sector

We know that in the right - triangle part of the figure adjacent to the sector, the height of the parallelogram (9 inches) is related to the radius $r$ of the sector by $\sin40^{\circ}=\frac{9}{r}$. So, $r=\frac{9}{\sin40^{\circ}}\approx\frac{9}{0.6428}\approx14$ inches.

Step3: Calculate area of the sector

The area formula for a sector of a circle is $A=\frac{\theta}{360^{\circ}}\times\pi r^{2}$, where $\theta = 40^{\circ}$ and $r\approx14$ inches. So, $A_{sector}=\frac{40^{\circ}}{360^{\circ}}\times\pi\times(14)^{2}=\frac{1}{9}\times\pi\times196\approx\frac{196\pi}{9}\approx\frac{196\times3.1416}{9}\approx68.6$ square inches.

Step4: Calculate total area of the figure

$A = A_{parallelogram}+A_{sector}=180 + 68.6=248.6$ square inches.

Answer:

248.6