Question in image

Question

Answer 1

So since they're asking for the lateral area, this means they want the surface area of this entire figure.

As a REGULAR HEXAGONAL PYRAMID, we can see in the figure we have 6 (corresponding to the 6 sides of the hexagon) equilateral triangles, and 1 hexagon to calculate the areas of to find the area of the entire figure.

triangles: we are given the BASE = 18ft, but the 22ft is not the side length of the triangle but the height, which is great! so together

6 triangles: BASE =18FT HEIGHT = 22 FT.

by the equation my lovely colleague Mark M. posted, we can calculate the total area of the triangles:

A_{one face} = (1/2)(base)(height)

Atotal of 6 triangles = 6 X (1/2) (18FT) (22FT) = 1188FT^2

hexagon: we're given the side length of the hexagon as LENGTH = 18FT

using the area of hexagon equation found on google, we can calculate that area as well

Area = (3√3 s²)/ 2 where s is the length of a side of the regular hexagon

Ahexagon = (3√3 18FT²)/ 2 = 841.8 FT^2 (rounded)

FINALLY, we add the areas of the 6 triangles to the area of 1 hexagon to get our final area

Agrand total = 1188FT^2 + 841.8 FT^2 = 2030. FT^2

Agrand total = 2030. FT^2

Answer 2

A_{one face} = (1/2)(base)(height)