Answer to Question #149294 in Geometry for KJ

Question #149294

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


1
Expert's answer
2020-12-08T10:10:06-0500

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



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