2.6. Find the area of regular polygon whose side and radius of inscribed
circle is given:
a =6cm n=5cm r= 5cm
Answers
Answered by
1
Answer:
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.
In area of a polygon some of the particular cases such as;
Similar questions