If in the figure above, semicircles

*X* and

*Y* have radii of 6 and 8 feet, respectively, then what is the area of semicircle

*Z* (in square feet)? (

**Note**: Figure not drawn to scale.)

A. 10π

B. 20π

C. 25π

D. 50π

E. 100π

(D) If the radii of the semicircles

*X* and

*Y* are 6 feet and 8 feet, then their diameters are 12 and 16 feet. These diameters are both lengths of the legs of a right triangle, and the diameter of semicircle

*Z* is the hypotenuse of this triangle.

The triangle is a 3-4-5 triangle, since the perpendicular legs are in the ratio 3 : 4. So the hypotenuse measures 20 feet, meaning the diameter of

*Z* is 20 feet and its radius is 10 feet.

To determine the area of semicircle

*Z*, we will determine the area of a full circle with the same radius as

*Z*, and then divide this quantity by 2.

The area of a circle with radius 10 is:

Area = π

*r*²

Area = π10² = 100π.

Thus, the area of semicircle

*Z* is 50π square feet. The correct answer is choice (D).

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** If the triangle is a 3:4:5,then shouldn't the legs of the triangle be 12, 16 and 25? The hypotenuse shouldn't be 20, it should be 25, correct? This means the radius is 25/2.**