Question

The of diagonals of a regular polygon is 35. What is the the area of the polygon if its apothem measures 10 centimeters?

Answer 1

Area of the polygon is `324.92(2dp)cm^2`

Explanation:

Let `n` be the number of sides of polygon; then `(n*(n-3))/2=35 or n^2-3n-70=0 or (n-10)(n+7)=0 :. n=10 or n=-7`. Number of diagonals can not be negative `:.n=10`. The polygon is decagon. we know area of the polygon `A_p= n*r^2.tan(180/n)`.Where `r` is the length of apothem.
`:.A_p= 10*10^2.tan(180/10) = 1000*tan18=324.92(2dp)cm^2`[Ans]