Find the area of an equilateral triangle with its height 8 cm ?

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Answer 1 · 2018-03-01T15:20:44

#"Area"=64/3~~21.3cm^2#

#"Area of an equilateral triangle"=1/2bh#, where:

We know/#h=8cm#, but we need to find the base.

For an equilateral triangle, we can find the value for half the base with Pythagoras.

Let's call each side #x#, half the base is #x/2#

#sqrt(x^2-(x/2)^2)=8#

#x^2-x^2/4=64#

#(3x^2)/4=64#

#x^2=64*4/3=256/3#

#x=sqrt(256/3)=(16sqrt(3))/3#

#"Area"=1/2bh=1/2x(x/2)=x^2/4=(sqrt(256/3)^2)/4=(256/3)/4=256/12=64/3~~21.3cm^2#