Answer to Question #148728 in Geometry for solid mensuration

Question

1. A frustum of a regular hexagonal pyramid has an upper base edge of 5m and a lower base edge of 8.5m. Its lateral area is 160m2. Determine the slant height of the frustum.

a) 2.53 m
b) 3.95 m
c) 4.25 m
d) 15 m

(with solution pls)

Answer 1

Consider frustrum of a regular hexagonal pyramid

Let $a_1=$ the upper base edge, $a_2=$ the lower base edge, and $L=$ the slant height.

The lateral area $A_L$ of the frustum of a regular pyramid is

$$A_L=\dfrac{1}{2}n(a_1+a_2)L$$

The lateral area $A_L$ of the frustum of a regular hexagonal $(n=6)$ pyramid is

$$A_L=\dfrac{1}{2}(6)(a_1+a_2)L$$

$$160=\dfrac{1}{2}(6)(5+8.5)L$$

$$L=\dfrac{160}{40.5}m\approx3.95 m$$

b) 3.95 m