Find the length of a regular Pentagon whose vertices lie on the circumference of a circle of radius 5 cm.
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Given : a regular Pentagon whose vertices lie on the circumference of a circle of radius 5 cm.
To Find : length of a side of Pentagon
Solution:
Central angle = 360°/5 = 72°
Radius = 5 cm
using cosine rule
a² + b² - 2abCosC = c²
Side of pentagon = x
=> x² = r² + r² - 2 r*rCos72°
=> x² =2r² - 2r²Cos72°
=> x² =2r²(1 - Cos72°)
=> x =1.17557 * r
=> x = 1.17557 * 5
=> x = 5.87785
length of a side of Pentagon = 5.87785 cm
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