Question

What is the number of diagonals in a (i) heptagon (ii) octagon (iii) polygon of 12 sides ?

Answer 1

We know that number of diagonal of polygon having n sides =$\frac{n(n-3)}{2}$ (i) In heptagon, no.of diagonals=$\frac{7(7-3)}{2}$=$\frac{7\times 4}{2}$=14 (ii) In octagon, no. of diagonals = $\frac{8(8-3)}{2}$ = $\frac{8\times 5}{2}$=20 (iii) In polygon of 12 sides = $\frac{12(12-3)}{2}$ = $\frac{12\times 9}{2}$=54