Let the number of sides of polygon be n Then total numbers of diagonal will be =nC2−n So, Given that Total number of diagonal is =44 ∴nC2−n=44 ⇒
n(n−1)
2
−n=44 ⇒n2−n−2n=88 ⇒n2−3n−88=0 ⇒n2−11n+8n−88=0 n(n−11)+8(n−11)=0 (n+8)(n−11) n=11,−8 We know that number of sides can not be negative. Hence total number of sides are 11 .