Find the area of the shaded region.

Question

Find the area of the shaded region. ​
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Quizplus · Accepted Answer

The shaded region consists of two semicircles and a rectangle.
The radius of each semicircle is 4 cm and the length of the rectangle is 6 cm.
Therefore, the area of each semicircle is 1/2 πr^2 = 1/2 π(4)^2 = 8π/2 = 4π cm^2
The area of the rectangle is length x width = 6 x 8 = 48 cm^2
Hence, the total shaded area is the sum of the areas of the semicircles and the rectangle which is:
2(4π) + 48 = 8π + 48 = 8(π+6) cm^2
Using a calculator, we get that 8(π+6) ≈ 37.7 cm^2
The closest answer choice is B: 11ea984b_b08e_a95f_9029_9f0ff5cd5f3d_TB4005_11.

Find the Area of the Shaded Region. ​

Find the Area of the Shaded Region.