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 isA. 432 cm2B. 216 cm2C. 180 cm2D. 144 cm2

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 :

BO2 = AB2 – AO2

BO2 = AB2 – AO2

BO2 = 152 – 122

BO2 = 225 – 144

BO2 = 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 cm2

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