Find the area of a regular 5-gon with a side of 2 cm.
| September 8, 2021 | education
Determine the value of the central angle AOB. The current as a pentagon is correct, then the angle AOB = 360/5 = 72.
The triangle AOS is isosceles, since OA = OB = R, then, by the cosine theorem:
AB ^ 2 = R ^ 2 + R ^ 2 – 2 * R * R * Cos72.
2 * R ^ 2 * (1 – Cos72) = AB2.
R ^ 2 = 4/2 * (1 – 0.31) = 2.9.
R = 1.7 cm.
Determine the area of the triangle AOB.
Saov = R2 * Sin72 / 2 = 1.37 cm2.
Then the area of the pentagon is: S = 5 * Saov = 5 * 1.37 = 6.85 cm2.
Answer: The area of the pentagon is 6.85 cm2.
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