How do you find the area of a 30, 60, 90, triangle?

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Answer 1 · 2015-06-16T21:13:32

1) #L^2/8sqrt(3)#
2) #b^2/2sqrt(3)#
3) #h^2sqrt(3)/6#

You know a 30-60-90 triangle is half an equilateral triangle, so the base is half of the hypotenuse L

#b=L/2#

You can use now Pythagoras theorem and calculate the height:

#h=sqrt(b^2 + L^2)= sqrt(L^2/4 + L^2)=sqrt(3/4L^2)=L/2sqrt(3)=bsqrt(3)#

So we can determine the area only knowing one of the edges:

1) If we know #L#:

#A=(bh)/2=1/2(L/2)(L/2sqrt(3))=L^2/8sqrt(3)#

2) If we know #b#:

#A=(bh)/2=b^2/2sqrt(3)#

3) If we know #h#:

#A=(bh)/2=1/2h^2/sqrt(3)=1/2h^2sqrt(3)/3=(h^2sqrt(3))/6#