The length of each side of an equilateral triangle is 14 \sqrt3 cm. What is the area of the incircle? (in cm^{2 })

SSC MTS Model Paper 1

Question : 33 of 150

Marks: +1, -0

The length of each side of an equilateral triangle is 14

√3

cm. What is the area of the incircle? (in cm

^{2 }

)

Solution:

BD=DC=7

√3

A D = √ { A B ^ { 2 } - B D ^ { 2 } }

= √ { ( 14 \√ { 3 } ) ^ { 2 } - ( 7 √ { 3 } ) ^ { 2 } } \\

= √ { ( 14 √ { 3 } + 7 √{ 3 } ) ( 14 √ { 3 } - 7 √ { 3 } ) }

= \√ { 21 \√ { 3 } \× 7 √ { 3 } } = 21 { cm }

∴OD=Radius of circle=

1/3

×21=7cm
∴Area of circle
=π

r^2

22/7

×7×7=154 sq.cm

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