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Question

Find the area of the equilateral triangle given below:

Given: AD=10 cm.

 



Your Answer
A

100 cm2

Your Answer
B

103 cm2

Your Answer
C

253 cm2

Correct Answer
D

10033 cm2


Solution

The correct option is A

10033 cm2


Let us assume AB=BC =AC =2a cm

Then BD =DC = a cm

In ΔABD,

AD2+BD2=AB2

102+a2=(2a)2 [Since AD = 10 cm]

4a2a2=100

3a2=100

a2=1003(1)

Area of equilateral triangle =34(side)2

=34(2a)2

=34.4a2

=3a2

=3.1003 [From (1)]

=10033 cm2
 

Alternate Solution:

Area of equilateral triangle with height h=h23

Area =1023=1003=10033 cm2

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