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Find the area of a rhombus having each side equal to 15 cm and one of whose diagonals is 24 cm.

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116 c m 2

160 c m 2

190 c m 2

216 c m 2

answer is D.

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Detailed Solution

Given a rhombus having each side equal to 15 cm and one of whose diagonals is 24 cm.
Prove that a parallelogram ABCD is a rhombus if and only if the diagonals AC and BD are perpendicular to each other. | Homework.Study.com

Prove that a parallelogram ABCD is a rhombus if and only if the diagonals AC and BD are perpendicular to each other. | Homework.Study.com

Using Pythagoras theorem in

Δ

OAB,

h y p o t e n u s e 2 = b a s e 2 + p e r p e n d i c u l a r 2 ⇒ A B 2 = O A 2 + O B 2

⇒ O B 2 = A B 2 − O A 2

⇒ O B 2 = 152 − 122

⇒ O B 2 = 225 − 144

⇒ O B 2 = 81

⇒ O B = 9 c m

Length of BD is,

⇒ B D = 2 × 9

⇒ B D = 18 c m

Let, area of the rhombus =

A = 12 × d i a g o n a l 1 × d i a g o n a l 2 ⇒ A = 12 × 24 × 18

⇒ A = 12 × 18

⇒ A = 216 c m 2

Therefore, the area is

216 c m 2

.
Hence, option 4 is correct.

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