Find the area of a rhombus one side of which measures 12 cm and one diagonal 13cm ........

Quantitative Aptitude (CDS) Mensuration 2D

Find the area of a rhombus one side of which measures 12 cm and one diagonal 13cm?

69 cm²

66 cm²

56 cm²

65 cm²

Let other diagonal = 2x

Since diagonals of a rhombus bisect each other at right angles, we have:

(13)² = (12)² + x²

x ² = (13)² – (12)²

x = $\sqrt{169-144}=\sqrt{25}$ = 5cm

So, other diagonal = 10 cm

Area of rhombus = 1/2 ×(product of diagonals)

= (1/2 × 10 ×13)cm² = 65cm²

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