It is known that the height of ladder ABCD is h. The two diagonals form angles of 30 degrees and 45 degrees respectively with the bottom to calculate the area of ladder
Trapezoidal ABCD, as AE ⊥ DC, DF ⊥ DC, < BDC = 30 °, ACD = 45 °,
BF/DF=tan30°,DF=BF/tan30°=√3h,
AE/CE=tan45°,CE=AE/tan45°=h,
CE+DF=DE+EF+EF+CF=CD+AB=h+√3h
The area of trapezoid ABCD = (CD + AB) * H / 2
=(h+√3h)*h/2
=(√3+1)h^2/2