Question

Find the area of the shaded portion. Show all work for full credit.6120

Answer 1

`\begin{gathered} \\ Triangles\text{ area=2(}\frac{\text{base }\cdot\text{ high}}{2}) \\ \text{base = 6} \\ \tan 60=(high)/(base) \\ \text{high}=\tan 60\cdot\text{base} \\ \text{high}=\tan 60\cdot(6) \\ \text{high}=10.39 \\ Triangles\text{ area=2(}\frac{(6)\text{ }\cdot(10.39)\text{ }}{2}) \\ Triangles\text{ area=62.34} \\ \text{circular sector area=}((6)\cdot(6\cdot2.1))/(2) \\ \text{circular sector area=37.8} \\ shaded\text{ area =}Triangles\text{ area-circular sector area} \\ shaded\text{ area =62.34-37.8} \\ shaded\text{ area =2}4.54 \\ \text{The shaded area is 24.54} \end{gathered}`