The length of side of a rhombus is 17 cm and one of its diagonals is 16 cm. Find the area of rhombus.

1. 120 cm

^{2}

2. 240 cm2

3. 360 cm2

4. 480 cm2

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Correct Answer – Option 2 : 240 cm2

Given:Length of side = 17 cm

Length of a diagonal = 16 cm

Concept used:The two diagonals bisect each other at 90° in a rhombus.

Formula used:Area of rhombus = (1/2) × Product of the two diagonals

Calculations:Let AC = 16 cm and BD = x cm

If the two diagonals of rhombus ABCD intersect at O then,

⇒ AO

^{2}+ BO^{2}= AB^{2}⇒ (16/2)

^{2}+ (x/2)^{2}= 17^{2}⇒ 64 + (x

^{2}/4) = 289⇒ (x

^{2}/4) = 225⇒ x

^{2}= 900⇒ x = 30 cm

Area of rhombus = (1/2) × 16 × 30

⇒ 8 × 30

⇒ 240 cm

^{2}∴The area of the rhombus is 240 cm^{2}