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

1 Answer
Jun 16, 2015

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

Explanation:

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