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Question

A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of Rs 5 per cm2. Find the cost of painting.


A
960
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B
480
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C
300
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D
192
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Solution

The correct option is A 960

All sides of a rhombus are equal
Therefore, AB = BD = DC = CA = 10 cm
Diagonal = 12 cm.
Since the diagonals bisect each other, BO = OC = 6 cm.
Now in AOC, AC = 10 cm, OC = 6 cm and AOC = 90°.
Using Pythagoras theorem,
AC2=AO2+OC2
AO2=AC2OC2=(10)2(6)2=10036=64=(8)2
Therefore, AO = 8 cm
Area of AOC = 12×base×height = 12 ×(OC)×(AO)
Area = 12×6×8 = 24 cm2
Area of the rhombus to be painted = 4 × Area of AOC
Area of painted rhombus = 4×24 cm2 = 96 cm2
Cost of painting per cm2 = Rs 5
Cost of painting of the entire rhombus = Rs 5×96 = Rs 480


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