Question

Please help!

Find the surface area of the pyramid to the nearest whole number.

Answer 1

two parts to this: find the area of one of the triangles making up the top, and find the area of the base. Any idea on how to proceed with either?

Answer 2

Would one of the triangles be 80?

Answer 3

Looks like it...

Answer 4

A couple of approaches for the base. There's certainly a formula involving the apothem, which they give us. Or, you could figure out 1/6 of the base as a pair of right triangles, given that you know the apothem and the length of the sides...

Answer 5

What is the formula?

Answer 6

For a regular \(n\)-sided polygon of side length \(s\) and apothem \(a\), the area is given by \[A = \frac{n s a}{2}\]where \(p\) is the perimeter.

Answer 7

what is the apothem?

Answer 8

If you go the triangle approach,

Answer 9

The apothem is the line from the center to the center of the side of the polygon

Answer 10

\[a=5\sqrt{3}\] in this problem

Answer 11

Ok, so my equation would be A = 6 * 10 * 5sqrt3 / 2

Answer 12

yes. and if you did the triangles, looking at my diagram, each 1/6th of the base would be \(\frac{1}{2} ( 5) 5\sqrt{3}\) which if multiplied by 6 gives you the same result.

Answer 13

Well, you add the area of the base, + 6 * the area of a side (because there are 6 sides)

Answer 14

i think I got it. It's 740 right?

Answer 15

Yes!