The length of each side of a rhombus is 10 cm. If the length of one of its diagonals is 16 cm, then what is the area of the rhombus?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 96 cm2.
Diagonals of a rhombus bisect each other at right angles.
Let ABCD be the rhombus, Diagonal AC = 16 cm, and side AB = 10 cm
In right △AOB, AB = 10 cm, AO = 8 cm
By Pythagoras' theorem, AB2 = AO2 + BO2
⇒ 102 = 82 + BO2
⇒ BO2 = 100 − 64 = 36
∴ BO = 6 cm
Diagonal BD = 2 × 6 = 12 cm
Area of Rhombus = 1/2 × (product of the diagonals)
= 1/2 × 16 × 12 = 8 × 12 = 96 sq.cm
Hence the Area of the rhombus = 96 sq. cm