Find the area of an equilateral triangle having altitude h cm.
the ared
LEVEL-2
Answers
Given : an equilateral triangle having altitude h cm
To find : area of an equilateral triangle
Solution:
Area of an Equilateral triangle = (√3 / 4)Side²
= (1/2) * Base * altitude
=(1/2) * Side * h
Let say side = a
Altitude on Equilateral triangle is Median also
Right angle triangle is formed
with sides a , h & a/2
Applying Pythagoras
=> h² = a² - (a/2)²
=> h² = a² - a²/4
=> h² = 3a²/4
=> a² = 4h²/3
=> a = 2h/√3
=> Side = 2h/√3
area of an equilateral triangle = (1/2) (2h/√3)h
= h²/√3
area of an equilateral triangle = h²/√3 cm² ( h is altitude )
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