Question

2. Find the area of a regular polygon whose side and r (a) n=7, a=5 cm, R=6 cm
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Answer 1

Answer:{n/2 × a × √(R² - a²/4)

Step-by-step explanation:

Area of a polygon of n sides

= n × (area ∆OAB) = n × ¹/₂ × AB × OL

= (ⁿ/₂ × a × r)

Now, A = 12 nar ⇔ a = 2Anr ⇔ na = 2Ar

⇔ Perimeter = 2Ar

From right ∆OLB, we have:

OL² = OB² - LB² ⇔ r² = {R² - (ᵃ/₂)²}

⇔ r = √(R² - (a²/4)

Therefore, area of the polygon = {n/2 × a × √(R² - a²/4) square units.