The area of a rhombus having one side 10 cm and one diagonal

Home » Aptitude » Mensuration » Question

The area of a rhombus having one side 10 cm and one diagonal 12 cm is

1. 48 cm.²
2. 96 cm.²
3. 144 cm.²
4. 192 cm.²

Correct Option: B

The diagonals of a rhombus bisect each other at right angles.
Let, AB = 10 cm.
AC = 12 cm.
∴ OA = OC = 6 cm.
∠AOB = 90°
∴ OB = √AB² - OA²
= √10² - 6² = √100 - 36
= √64 = 8 cm.
∴ BD = 2 × OB = 16 cm.

∴ Area of rhombus =	1	d₁d₂
	2

=	1	× 12 × 16 = 96 sq. cm.
	2