Question

The lower base of the frustum shown in the figure is a square 8ft on each side. The upper base is a square 4ft on each side. In the altitude is 6ft, find the slant height
A- 4ft
B- 5.66 ft
C- 6 ft
D- 6.32 ft

Answer 1

The answer is D 6.32
S= the slant Height
Then we need to get the apothem of the lower and upper base
S^2 = (apothem of the lower base - apothem of the upper base)^2 + (height)^2 
and they would be like this:
apothem of the lower base = 8 / 2*tan(90/2) = 4 
apothem of the upper base = 4 / 2*tan(90/2) = 2 
S^2 = (4 - 2)^2 + (6)^2 
S^2 = 2^2 + 6^2 
S^2 = 4 + 36 
S^2 = 40 
S = 6.32