# Find the area of a sector of a circle having

Find the area of a sector of a circle having radius r and central angle $$\displaystyle\theta$$. Express answers to the nearest tenth. $$\displaystyle{r}={29.2}\ {m},\ \theta={\frac{{{5}\pi}}{{{6}}}}$$ radians

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Leory2000
The area A of a sector of a circle of radius r formed by a central angle with radian measure $$\displaystyle\theta$$ is
$$\displaystyle{A}={\frac{{{1}}}{{{2}}}}{r}^{{2}}\theta$$
Substitute r=29.2 m, $$\displaystyle\theta={\frac{{{5}\pi}}{{{6}}}}$$ and solve for A
$$\displaystyle{A}={\frac{{{1}}}{{{2}}}}{\left({29.2}\ {m}\right)}^{{2}}\cdot{\frac{{{5}\pi}}{{{6}}}}$$
Use a calculator
$$\displaystyle{A}\approx{1116.1}\ {m}^{{2}}$$
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