SSC CGL Tier II 12 Jan 2017 Paper 1

Question : 57 of 100

Marks: +1, -0

The area of a rhombus having one side 10 cm and one diagonal 12 cm is

Solution:

(2)

The diagonals of a rhombus bisect each other at right angles.
Let, AB = 10 cm.
AC = 12 cm.
∴ OA = OC = 6 cm.
∠AOB = 90°

∴ { OB } = √ { { AB } ^ { 2 } - { OA } ^ { 2 } }

=√{ 10 ^ { 2 } - 6 ^ { 2 } } = √ { 100 - 36 }

= √{ 64 } = 8 { \cm } .

∴ { BD } = 2 × { OB } = 16 { \cm }

∴ Area of rhombus =

{ 1 }/ { 2 } d _ { 1 } d _ { 2 }

=1/2 × 12 × 16 = 96

sq. cm.

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