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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.

 

 Jun 6, 2024

Best Answer 

 #1
avatar+1946 
+1

The diameter of AB is 9+16+9=34. This means the radius is 34/2=17

 

However, let's note something. 

QD=9(9+16)=15, but in the problem, it says the square sidelenghth is 16. This means that PQRS is NOT a square, but a rectange with sidelengths 16 and 15. 

 

Like I said, the diameter is 34. We already know the height of the trapezoid, which we got earlier as 15. DC is 16, since PQRS is a rectangle. 

 

We have everything we need to solve for the area of the trapezoid! 

 

The area of a trapezoid is (b1+b2)h2 where b1 and b2 are the bases and h is the height. 

 

We have (25+16)152=(31)15/2=232.5

 

so the area of the trapezoid is 232.5. 

 

Thanks! :)

 Jun 6, 2024
 #1
avatar+1946 
+1
Best Answer

The diameter of AB is 9+16+9=34. This means the radius is 34/2=17

 

However, let's note something. 

QD=9(9+16)=15, but in the problem, it says the square sidelenghth is 16. This means that PQRS is NOT a square, but a rectange with sidelengths 16 and 15. 

 

Like I said, the diameter is 34. We already know the height of the trapezoid, which we got earlier as 15. DC is 16, since PQRS is a rectangle. 

 

We have everything we need to solve for the area of the trapezoid! 

 

The area of a trapezoid is (b1+b2)h2 where b1 and b2 are the bases and h is the height. 

 

We have (25+16)152=(31)15/2=232.5

 

so the area of the trapezoid is 232.5. 

 

Thanks! :)

NotThatSmart Jun 6, 2024

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