Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
If a circle touching all the $n$ sides of a polygon of perimeter $2 p$ has radius $r$, then the area of the poly-gon is
(a)$(p-n) r$
(b)pr
(c)$(2 p-n) r$
(d)$(p+n) r$
Answer
Answer (as printed): B
Explanation
Let $A B$ be a side of the polygon and $O$ be the centre of the circle. Let $O M \perp A B$. Perimeter $=2 p \Rightarrow A B=\frac{2 p}{n}$. ∴ Area of the polygon $=n \times$ area $(\Delta O A B)=n \times \frac{1}{2} A B \times O M=n \times \frac{1}{2} \times \frac{2 p}{n} \times r=p r$.
Explanation as extracted from the printed page; notation may be imperfect.