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.
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! :)
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! :)