Question

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question
find the area of the figure below, composed of a parallelogram and two semicircles. round to the nearest tenths place.
(image of the figure with dimensions 10, 6, 8)

Explanation:

Step1: Analyze the figure components

The figure is composed of a parallelogram and two semicircles. Notice that the two semicircles can form a full circle. First, find the area of the parallelogram and the area of the circle formed by the two semicircles, then sum them.

Step2: Area of the parallelogram

The formula for the area of a parallelogram is \( A = base \times height \). From the figure, the base of the parallelogram is \( 10 \) and the height is \( 6 \). So, \( A_{parallelogram} = 10 \times 6 = 60 \).

Step3: Area of the circle (from two semicircles)

The diameter of each semicircle is \( 8 \), so the radius \( r = \frac{8}{2} = 4 \). The formula for the area of a circle is \( A = \pi r^2 \). Substituting \( r = 4 \), we get \( A_{circle} = \pi \times 4^2 = 16\pi \approx 16 \times 3.1416 = 50.2656 \).

Step4: Total area of the figure

Sum the area of the parallelogram and the area of the circle: \( A_{total} = 60 + 50.2656 = 110.2656 \).

Step5: Round to the nearest tenths place

Rounding \( 110.2656 \) to the nearest tenths place, we look at the hundredths digit which is \( 6 \). Since \( 6 \geq 5 \), we round up the tenths digit. So, \( 110.2656 \approx 110.3 \).

Answer:

\( 110.3 \)