Engineering Board Exam Reviewer · Areas of Plane Figures · medium
Semicircles are drawn outward on the legs of a right triangle with legs 6 and 8, and a semicircle is drawn outward on the hypotenuse. Find the combined area of the two crescents (lunes) lying outside the large semicircle.
- 48
- 12
- 18.85
- 24
Answer
D. 24
Solution
Lunes = (semicircles on the legs) + triangle - (semicircle on the hypotenuse). Since 62+82=102, the semicircle areas cancel, leaving the triangle area 12(6)(8)=24.
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