Question

The adjacent sides of a parallelogram are 8 cm and 9 cm a diagonal joining the ends of the sides is 13 cm calculate the area of parallelogram

Answer 1

let tqo adjacent sides are a=8cm, b=9cm
diagonal d=13cm
these three sides show one triangle
s= (a+b+c)/2=(8+9+13)/2=30/2=15
s-a=15-8=7
s-b=15-9=6
s-c=15-13=2
area of the triangle = root [s(s-a)(s-b)(s-c)
= root[15*7*6*2
area of the parallelogram =2*area of triangle
=2*[root(15*7*6*2)]
simplify it

Answer 2

let parallelogram is ABCD
AB=8 , BC=9.In parallelogram opposide sides are equal then AB=DC , BC=AD
diagonal =13 assume it as AD
area of parallelogram = area of triangle ACD+area of triangle ACB
area of ACD=36
area of ACB=36
area of parallelogram =36+36=72