Q. 10

# Each side of a rhombus is 15 cm and the length of one of its diagonals is 24 cm. The area of the rhombus is

A. 432 cm^{2}

B. 216 cm^{2}

C. 180 cm^{2}

D. 144 cm^{2}

Answer :

Given: A rhombus ABCD

Diagonal AC = 24 cm

Side length : AB = BC = CD = DA = 15 cm

We know that diagonals of the rhombus bisect each other right angles.

AO = AC

⇒AO = ( × 24) cm

⇒AO = 12 cm

From right AOB, we have :

BO^{2} = AB^{2} – AO^{2}

⇒BO^{2} = AB^{2} – AO^{2}

⇒BO^{2} = 15^{2} – 12^{2}

⇒BO^{2} = 225 – 144

⇒BO^{2} = 81

⇒BO = 9 cm

BD = 2 × BO

BD = 2 × 9 = 18 cm

Hence, the length of the other diagonal is 18 cm.

Area of the rhombus = × 24 × 18 = 216 cm^{2}

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