Quoted By:
wrong board but :
move the bottom triangle to the top, middle area is 6*L
so 6*L = (s*d)/2
sin(?) = s/L (big triangle)
sin(?) = 6/c = 6/(s-d) (small triangle)
s/L = 6/(s-d)
s = 6L/(s-d)
s(s-d) = 6L
s(s-d) = (s*d)/2
s^2 - s*d = (s*d)/2
s^2 = 3/2 * (s*d) divide by s both sides
s = 3/2 * d or the other way d = 2/3 * s
hence c = 1/3 * s
tan(?) = 6/b (small triangle)
tan(?) = s/d = s/(2/3 * s) = 3/2 (big triangle)
3/2 = 6/b
b = 6 * 2/3 = 4
c^2 = 6^2 + b^2 (small triangle)
c^2 = 36 + 16
c = sqrt(52)
s = 3*c
area = s^2 = (3*c)^2 = 9*52 = 468
