If the altitude in the equilateral triangle is 6 cm,then find the area of an equilateral triangle.
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Answer:
In right angle △ADB, Using Pythagones theorem,
⇒(
2
a
)
2
+(
6
)
2
=a
2
⇒
4
a
2
+6=a
2
⇒
4
3a
2
=6⇒a
2
=8⇒a=2
2
cm
∴ △ABC (equilateral △) =
4
3
a
2
=
4
3
×2
2
×2
2
=2
3
cm
2
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