Math, asked by sanghaniasmita364, 10 months ago

Find the area of an equilateral triangle having altitude h cm.
the ared
LEVEL-2​

Answers

Answered by amitnrw
0

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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