✏️SECTOR
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Problem: Find the area of the shaded region given m∠SAT = 90° and the radius of circle A is 12cm. Show your complete solution.
Solution: Find the area of the product of the circle's area and the ratio of the central angle at 360 degrees.
[tex] \begin{aligned}& \bold{ \color{lightblue}Formula:} \\ & \boxed{A_{seg} = \frac{ \theta}{360 \degree} \cdot\pi {r}^{2} } \end{aligned}[/tex]
- [tex] \begin{aligned}{A_{seg} = \frac{90 \degree}{360 \degree} \cdot\pi (12cm)^{2} } \end{aligned}[/tex]
- [tex] \begin{aligned}{A_{seg} = \frac{1}{4} \cdot\pi (144cm^{2}) } \end{aligned}[/tex]
- [tex] \begin{aligned}{A_{seg} = \frac{\pi (144cm^{2}) }{4} } \end{aligned}[/tex]
- [tex] \begin{aligned}{A_{seg} = \pi (36cm^{2}) } \end{aligned}[/tex]
- Let 3.14 be the approximate value of pi.
- [tex] \begin{aligned}{A_{seg} ≈ (3.14) (36cm^{2}) } \end{aligned}[/tex]
- [tex] \begin{aligned}{A_{seg} ≈ 113.04cm^{2} } \end{aligned}[/tex]
- Therefore, the area of the sector is:
- [tex] \large \rm Sector \: Area = \boxed{ \rm \green{ \: 113.04 \: sq. \: cm \: }}[/tex]
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