+1046 Trapezoid $ABCD$ is inscribed in the semicircle with diameter $\overline{AB}$, as shown below. Find the radius of the semicircle. Find the area of ABCD.
PQDC is a square.
0 Label the mid-point of \(AB\), \(M\)
\(\triangle MPC\) has \(MC\) as the radius,\(PM=8\), and \(CP=16\), BY pythagorean theoreom on said triangle we get:
\(MC=\sqrt{PM^2+CP^2}\\ \boxed{MC=8\sqrt5}\)
+38 To find the area of a trapazoid, we need the find the height and the average of the bases of the trapazoid. The height of the trapazoid is \(16\). The average of the bases is \(25\). \(\dfrac{25 \cdot 16}{2}=200 \). And now, we're done! 
Hope this helped!
