Question

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Answer 1

The area of the shaded region is 3.125π - 6. The correct option is E. 3.125π - 6

Calculating area

From the question, we are to determine the area of the shaded region

The area of the shaded region = Area of the semicircle - Area of the triangle

First, we will determine the diameter, d, of the semicircle

d² = 3² + 4² (Pythagorean theorem)

d² = 9 + 16

d² = 25

d = √25

d = 5

∴ Diameter of the semicircle is 5

Thus,

Radius, r = 5/2 = 2.5

Now,

Area of the shaded region = 1/2(π×2.5²) - 1/2(3×4)

Area of the shaded region = 1/2(π×6.25) - 1/2(12)

Area of the shaded region = 3.125π - 6

Hence, the area of the shaded region is 3.125π - 6. The correct option is E. 3.125π - 6

Learn more on Calculating area here: brainly.com/question/14989383

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