Find the area. Round your answer to the nearest hundredth if necessary.
-Find the area of a regular decagon (10 sides) inscribed in a circle of radius 10 inches.
A) $500 \sin 45 ^ { \circ } \approx 353.55$ square inches
B) $500 \sin 36 ^ { \circ } \approx 293.89$ square inches
C) $1000 \sin 36 ^ { \circ } \approx 587.79$ square inches
D) $500 \cos 36 ^ { \circ } \approx 404.51$ square inches

Question

Quizplus · Accepted Answer

The area of a regular decagon inscribed in a circle can be calculated using the formula $Area = \frac{1}{2}nR^2\sin\left(\frac{360}{n}\right)$, where $n$ is the number of sides (10 for a decagon) and $R$ is the radius of the circle. Substituting $n = 10$ and $R = 10$ inches, the formula simplifies to $Area = 500 \sin 36 ^ { \circ }$, which matches choice B.

Find the Area 500sin⁡45∘≈353.55500 \sin 45 ^ { \circ } \approx 353.55500sin45∘≈353.55

Find the Area $500 \sin 45 ^ { \circ } \approx 353.55$