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Purple Comet 2018 HS problem 9

Source:

March 19, 2020
geometry

Problem Statement

trapezoid has side lengths 10,10,1010, 10, 10, and 2222. Each side of the trapezoid is the diameter of a semicircle with the two semicircles on the two parallel sides of the trapezoid facing outside the trapezoid and the other two semicircles facing inside the trapezoid as shown. The region bounded by these four semicircles has area m+nπm + n\pi, where m and n are positive integers. Find m+nm + n. https://3.bp.blogspot.com/-s8BoUPKVUQk/XoEaIYvaz4I/AAAAAAAALl0/ML0klwHogGYWkNhY6maDdI93_GkfL_eyQCK4BGAYYCw/s200/2018%2Bps%2Bhs9.png
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