prove that the area of an equilateral triangle is equal to a^2/4 IF SIDE OF EQUILATERAL TRIANGLE IS A
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Proof- Since all the 3 sides of an equilateral triangle are same AB=BC=CA=a
For altitude of △ABC
Draw a ⊥ from point C on AB.
So that CO⊥AB. Let OC=h
In △AOC
By using Pythagoras Theorem
AC
2
=AO
2
+OC
2
OC
2
=AC
2
−AO
2
h
2
=a
2
−(
2
a
)
2
h
2
=a
2
−
4
a
2
h
2
=
4
3a
2
⇒h=
2
3
a
Now Area of △ABC=
2
1
×Base×Height
=
2
1
×a×
2
3
a
Area =
4
3
a
2
So Area of equilateral △ comes is
4
3
a
2
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