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Question
Find the area of an equilateral triangle having altitude h cm.
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Solution
Altitude of a equilateral triangle, having side a is given by
Altitude = `sqrt(3)/2 a`
Substituting the given value of altitude h cm, we get
`h = sqrt(3)/2 a`
`a = 2/sqrt( 3) h cm `
Area of a equilateral triangle, say A having each side a cm is given by
`A= sqrt(3)/4 a^2`
Area of the given equilateral triangle having each equal side equal to `2/sqrt(3) h cm ` is given by;
`A = sqrt(3)/4 ( 2/sqrt(3) h cm )^2`
`A = sqrt(3)/4 xx 4/3 h^2`
`A = h^2/sqrt(3)cm ^2`
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