Question:
If the side of a rhombus is 10 cm and one diagonal is 16 cm, then area of the rhombus is 96 cm2.
Solution:
True
Given, side of a rhombus PQRS is 10 cm and one of the diagonal is 16 cm.
i.e., PQ = QR = RS =SP = 10 cm and PR = 16 cm
In ΔPOQ, PQ2 = OP2 + OQ2 [by Pythagoras theorem]
[ since, the diagonal of rhombus bisects each other at 90°] => OQ2 = PQ2 – OP2 = (10)2 – (8)2
=> OQ2 =100 – 64 = 36
=> OQ = 6 cm
[taking positive square root because length is always positive] SQ =2 x OP = 2 x 6= 12 cm
Area of the rhombus = ½ (Product of diagonals)
= ½ (OS x PR) =½ x 12 x 16 = 96 cm2.