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Question

Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.


A

240 cm2

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B

480 cm2

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C

400 cm2

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D

550 cm2

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Solution

The correct option is A

240 cm2


ABCD is a rhombus in which AB = BC = CD = DA = 17 cm
AC = 16 cm

Therefore, AO = 8 cm (Diagonals of a rhombus bisect each other at 90.)
In ∆AOD,
AD2 =AO2 + OD2
172 = 82 +OD2
⇒ 289 = 64 + OD2
⇒ 225 = OD2
⇒ OD = 15
Therefore, BD = 2 OD
= 2 × 15
= 30 cm
Hence, area of rhombus
= 12 × 16 × 30
= 240 cm2


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