I need help with finding the surface area of a regular hexagonal pyramid. Im attaching the picture of the problem. PLEASE HELP

Question

anonymous · Answer

attachment

whpalmer4 · Answer

Okay, this turns out to be pretty easy, you just need to find the area of a whole bunch of triangles!

Let's tackle the upper surface first.  It is made up of 6 triangles, can you identify the height and base dimensions of those 6 triangles?

anonymous · Answer

ok, so you know that there are 6 triangles

anonymous · Answer

and you know that the height of these triangles is 10

anonymous · Answer

so now we have 12 triangles with height 10

anonymous · Answer

where the base is 4rad3

anonymous · Answer

use pythagerms thm. to figure out the missing side

whpalmer4 · Answer

no need to find the missing side — we just want the area of the triangle, and that's just $$A=\frac{1}{2}bh$$

whpalmer4 · Answer

also, the base of those triangles is 8 m — the $4\sqrt{3}$ refers to the apothem - distance from the center of the base to the middle of one of the sides.

anonymous · Answer

@whpalmer4 I need the answer

whpalmer4 · Answer

Well, then you need to start taking part in the discussion!

anonymous · Answer

fml haha okay i tried. is it 240??    @whpalmer4

whpalmer4 · Answer

Now OS is being sluggish for me :-(

240 is area of the top, yes!  Now how about the base, any idea how to do that?

whpalmer4 · Answer

So the base looks like this:

whpalmer4 · Answer

it looks like there are 6 triangles, each with base $8$ and height $4\sqrt{3}$. if you can find the area of one of those triangles, multiply by 6 (to cover the entire base) and add to the 240 you got for the upper surface, you'll have the answer!

whpalmer4 · Answer

remember, $$A = \frac{1}{2}b h$$