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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.

 

 Feb 24, 2024
 #1
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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:
\(MC=\sqrt{PM^2+CP^2}\\ \boxed{MC=8\sqrt5}\) 

 Feb 25, 2024
 #3
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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! smiley Hope this helped!

 Feb 27, 2024

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