Question

the figure shown is a rectangle with a semicircle on each end. what is the area of the figure? use 3.14 for π and round your answer to the nearest tenth. 8 in. 6 in. 161.0 in.² 76.3 in.² 104.5 in.² 34.8 in.²

Explanation:

Step1: Calculate rectangle area

The rectangle has length $l = 8$ in and width $w=6$ in. The area of a rectangle is $A_{rect}=l\times w$. So $A_{rect}=8\times6 = 48$ in².

Step2: Calculate area of two - semi - circles

The two semi - circles at the ends form a complete circle. The diameter of the circle is equal to the width of the rectangle, so $d = 6$ in and the radius $r=\frac{d}{2}=\frac{6}{2}=3$ in. The area of a circle is $A_{circle}=\pi r^{2}$. Using $\pi = 3.14$, we have $A_{circle}=3.14\times3^{2}=3.14\times9 = 28.26$ in².

Step3: Calculate total area

The total area of the figure $A = A_{rect}+A_{circle}=48 + 28.26=76.26\approx76.3$ in².

Answer:

$76.3$ in²