Question 1155099
<br>
Draw altitude XA.  Because XYZ is an isosceles triangle, XA divides triangle XYZ into two congruent right triangles, each with hypotenuse 25 and one leg 20.  The makes the length of XA 15.<br>
Now draw AB, where B is the point of tangency of the semicircle with side XY.  AB is a radius of the semicircle.<br>
Triangles XAY and ABY are similar, since both are right triangles sharing angle Y.  By similar triangles,<br>
{{{AB/AY = XA/XY}}}
{{{AB/20 = 15/25}}}
{{{AB = 12}}}<br>
The radius of the semicircle is 12; its area is<br>
{{{(1/2)(pi)(r^2) = (1/2)(pi)(12^2) = 72pi}}}<br>