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Determine the shaded area.The shaded area is(Type an integer or decimal rounded to the nearest hundredth

Determine the shaded area.The shaded area is(Type an integer or decimal rounded to-example-1
User Jgbarah
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The shaded area is equal to the area of the circle substracted fromt he area of the trapezoid:


A=A_T-A_C

Area of a trapezoid:


A_T=((a+b))/(2)\cdot h

a is long base

b is short base

h is height

Area of a circle:


A_C=\pi\cdot r^2

The given trapezoid has a height equal to 2 times the radius of the circle in it. Then, the area of the shaded area is:


A=((a+b))/(2)\cdot2r-\pi\cdot r^2

a=13in

b=9in

r=3in


\begin{gathered} A=((13in+9in))/(2)\cdot2(3in)-\pi\cdot(3in)^2 \\ \\ A=((22in))/(2)\cdot6in-9\pi in^2 \\ \\ A=66in^2-9\pi in^2 \\ \\ A\approx37.73in^2 \end{gathered}

User Gabriel Ittner
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