Question

I am trying the find the area of a lune and show that it equals the area of a right triangle inside of quarter circle. I have for the area of the semi circle containing the lune. Then I found the area of the quarter circle and the area of the right triangle in the quarter circle. Next I subtracted the area of the triangle from the quarter circle to get the excess shaded area between the lune and the triangle. Then I subtracted the excess area from the semicircle containing the lune. However I do not get that the lune is equaled to the right triangle. Can you tell me if I'm on the right track?

Answer 1

Would appreciate knowing how your drew the lune, i.e. the geometry of the lune. This is the key to your problem.