Final answer:
The area of the shaded region is calculated by subtracting the area of the trapezoid from the area of the circle, resulting to 105.1 square cm.
Step-by-step explanation:
First, you need to find the area of the circle as it encompasses the entire figure. As the diameter is made up of two sides of the trapezoid, which are each 8cm, the diameter of the circle is 16cm. Using the formula to calculate the area of the circle, Area= πr^2 (π times radius squared), where radius (r)=(diameter / 2)=8cm, it follows that the area of the circle is 201.1 square cm (π*8*8=201.1).
Next, calculate the area of trapezoid ABCD where AB=AD=BC=8cm. Since ABCD is an isosceles trapezoid, the formula for finding the area is Area = 0.5(a+b)h where a and b are the bases, and h is the vertical height. Here, the bases are AB and CD, and the height is the radius of the circle which is 8cm. Now, BC=8cm=radius=height and CD=16cm=twice the radius=twice the height. Hence, the area of the trapezoid is 96 square cm (0.5*(8+16)*8=96).
The shaded region is that portion of the circle outside the trapezoid. Hence, the area of the shaded region would be the difference between the area of the circle and the area of the trapezoid which equates to 105.1 square cm (201.1 - 96).
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