Question

The lateral area of a regular pyramid with an octagonal base is 109.9 cm2. If the slant height is 6.7 cm, find the length of one side of the base. Round to the nearest tenth.
A 2.1 m
B 16.4 m
C 32.8 m
D 4.1 m

Answer 1

Given pyramid with octagonal base. Image of the pyramid attached below:

We know the formula of Lateral Area of pyramid = $\frac{1}{2} pl$

where p represent the perimeter of the octagonal base

and l represent the slant height of the pyramid.

109.9 = $\frac{1}{2}*p*6.7$

Solve for p

p = 32.81 cm

Perimeter of octagonal base (all sides are same) = 8*s

where s represent the side of octagon

8s = 32.81

Solve for s

s = 4.1 cm

Side of the octagon = 4.1cm (option D)