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Question

A rhombus having each side 10 cm has one of its angles as 120, then the area of the rhombus will be equal to


A

1003 cm2

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B

503 cm2

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C

1503 cm2

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D

753 cm2

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Solution

The correct option is B

503 cm2


Let ABCD be the rhombus in which AB=AD=10 cm B=120 as shown in figure

A=180120=60

Draw DE perpendicular to AB

In Δ AED, A=60, AED=90, ADE=30

The corresponding sides can be calculated as

sin(30):sin(60):sin(90)

12:32:1

1:3:2

In a 30-60-90 right angled triangle, the sides are in the ratio 1 : 3 : 2

i.e AE : DE : AD = 1 : 3 : 2

Hence, let the sides be x , 3x , 2x

Given, 2x = 10 cm, x = 5 cm

Therefore DE = 53 cm

Area of rhombus = AB×DE

=10×53=503 cm2


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