✒️AREA
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[tex] \large\underline{\mathbb{ANSWER}:} [/tex]
[tex] \qquad \Large \: \rm{\approx 38.05 \: sq. \: cm} [/tex]
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[tex] \large\underline{\mathbb{SOLUTION}:} [/tex]
» By constructing radii to each corner of the Pentagon, we have created five congruent triangles.
- 5 identical isosceles triangles
- Each apexes measures 72°
» Find the area of one of the isosceles triangles.
[tex] \begin{align} & \bold{Formula:} \\ & \quad \boxed{\rm A_{\,Triangle} = \frac{\,1\,}{2} \cdot r^2 \sin\theta} \end{align} [/tex]
- [tex] A_{\,Triangle} = \frac{\,1\,}{2} \cdot (4)^2 \sin72\degree \: cm^2 \\ [/tex]
- [tex] A_{\,Triangle} = \frac{\,1\,}{2} \cdot 16 \sin72\degree \: cm^2 \\ [/tex]
- [tex] A_{\,Triangle} \approx \frac{\,1\,}{2} \cdot 15.22 \: cm^2\\ [/tex]
- [tex] A_{\,Triangle} \approx 7.61 \: cm^2 \\ [/tex]
» Multiply the approximate area of the triangle to 5 to find the area of the shaded region or the area of the Pentagon inscribed in the circle.
- [tex] 7.61(5) \: cm^2 \approx 38.05 \: cm^2 [/tex]
[tex] \therefore [/tex] The area of the shaded region inside the circle is about 38.05 cm²
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(ノ^_^)ノ
