The illustration of the problem is shown in the picture. First, let's find the area of the triangle through Heron's law.
A = √s(s-a)(s-b)(s-c)
where
s = (a+b+c)/2
a, b and c are the measures of the sides of the triangle
s = (1+1+1)/2 = 1.5
A = √1.5(1.5-1)(1.5-1)(1.5-1)
A = 0.433 m³
The other formula for area of triangle is:
A = 1/2*base*height = 0.433 m³
0.433 = 1/2*1*h
h = 0.866 m
