Answer
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Step 1:: Identify the shapes and their dimensions in the given figure.
The height of the triangle is 4 units ($$h = 4$$).
The figure consists of a semicircle and a right triangle. The diameter of the semicircle is also the base of the triangle.
Step 2:: Calculate the area of the semicircle.
A_{semicircle} = frac{1}{2}pi (3)^2 = frac{1}{2}pi 9 = 4.5pi
Plugging in the values, we get:
Step 3:: Calculate the area of the triangle.
A_{triangle} = frac{1}{2}(6)(4) = 12
Plugging in the values, we get:
Step 4:: Subtract the area of the triangle from the area of the semicircle to find the area of the shaded region.
A_{shaded} = A_{semicircle} - A_{triangle} = (4.5pi) - 12
Final Answer
The area of the shaded region is (4.5pi) - 12 square units, or approximately 1.57 square units when rounded to two decimal places.
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