Question

a regular hexagonal pyramid has a base area 166.28 square feet, slant height of 9.8 feet, and a surface area of 401.48 square feet, find side length of the base

Answer 1

This is the concept of surface area of the solid figures, we are required to find the length of the side of a hexagonal base pyramid.
The base area is given by 166.28 ft^2.
This implies that the base area of the polygon is 166.28 ft^2
To get the length of the sides we proceed as follows;

Area of hexagon is given by:
Area=(a)[3sqrt3]/2
where a is the side length
this can be written as:
Area=2.6a^2
Hence;
2.6a^2=166.28
dividing both sides by 2.6 we get:
a^2=64.00012
thus a=sqrt(64.0012)=8.000075 ft
therefore the side length is 8 ft