Geometry

Quantitative Aptitude (CPO)

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One side of a rhombus is 13 cm and one of its diagonals is 24 cm. What is the area of the rhombus?

This questions was previously asked in

SSC CPO 12th-March-2019-Shift-2

120 cm²

130 cm²

156 cm²

312 cm²

- A rhombus has all sides of equal length. Here, one side is given as 13 cm.

- One diagonal is given as 24 cm.

- Diagonals of a rhombus bisect each other at right angles.

- We can find the other diagonal using the Pythagorean theorem. Half-diagonals form a right triangle with the side: \( (13^2 = (12)^2 + (d/2)^2) \).

- Solve to find \( d/2 = 5 \), so the other diagonal, \( d = 10 \).

- Area of a rhombus = \((1/2) \times \text{Diagonal 1} \times \text{Diagonal 2} = (1/2) \times 24 \times 10 = 120 \).

- Options:

- Option 1: 120 cm²

- Option 2: 130 cm²

- Option 3: 156 cm²

- Option 4: 312 cm²