One diagonal of a rhombus is $8\sqrt{3}$ cm . If the other diagonal is equal to its side, then the area (in cm2) of the rhombus is :
Answer & explanation
Correct answer: option 4
We know that,
The diagonals of a rhombus bisect each other at right angles.
Area of a rhombus = \(\frac{1}{2}\) × Diagonal1 × Diagonal2
Given,
D1 = 8\(\sqrt {3}\) cm
D2 = side of the rhombus = a
By Pythagoras theorem
a2 = \(\frac{a^2}{4}\)+ (4\(\sqrt {3}\))2
= a2 = 64
= a = 8 cm = D2
The area of the rhombus = \(\frac{1}{2}\) × 8 × 8\(\sqrt {3}\)=32\(\sqrt {3}\) cm2