a regular hexagonal pyramid of altitude is 12 meters and whose base edge is 3 meters is cut by a plane parallel to its base and is 3 meters from the base. What is the lateral area of a frustum formed?

Solution:

The lateral area is sum of area of six same trapezoids

The one base of the trapezoid is 3 meters, another base is X

X/3 = (12-3)/12, X = 9/4 = 2.25 meters

The height of trapezoid =  1/4 * sqrt(12^2 + [3sqrt(3)/2]^2) = 3.07 meters

Area of one trapezoid = (3+2.25)*3.07/2 = 8.059 square meters

The lateral area = 6*8.059 = 48.35 square meters