Answer:
Lateral: 560
Surface Area: [tex]560 + 96\sqrt{3}[/tex]
Step-by-step explanation:
Well, we know that the lateral area is just the surface area subtracted by the hexagon base of the figure. Thus, if we (1) find the area of one of the triangular faces and multiply by 6, we get the lateral area. And then, if we (2) add the area of the hexagonal base, we get the surface area.
Let's do (1) first to get the lateral area
They mention that the base of one of the triangular faces is 8 and its height (which is the slant height) is 20. So the area is simply 20 * 8/2 = 80
Then, we multiply by 6 because there are 6 of these triangles and get 560
So the lateral area is 560
Let's do (2) next to find the surface area
If we add the area of the hexagonal base to 560, we obtain the surface area
The hexagon is a regular hexagon with a length of 8. Now, the area of a hexagon [tex]3\sqrt{3} * s^2 /2[/tex] where [tex]s[/tex] is the side. We can obtain this formula if we separate the hexagon into 6 equilateral triangles.
Plugging in 8 for [tex]s[/tex] we get [tex]96\sqrt{3}[/tex]
So the surface area is [tex]560 + 96\sqrt{3}[/tex]
