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 cm2
B. 216 cm2
C. 180 cm2
D. 144 cm2
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 :
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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