Finding Surface Area and Volume of a Pyramid

[isu23pink]

okay so i did this problem TWICE, followed the formula and everything.
[attachment=1:xpjx7d77]b.JPG[/attachment:xpjx7d77]

i did the problem TWICE, but still keeping getting it wrong! here's my work:
[attachment=0:xpjx7d77]b1.jpg[/attachment:xpjx7d77]

someone help me please!

 

[mmm4444bot]

You correctly found the height of the triangular face:

x = 2 sqrt(7)

I'm not sure why you then wrote (1/2)(48)(8) for the area of the triangular face.

A = (1/2)(12)(2 sqrt[7]) = 12 sqrt(7)

There are four triangular faces.

4A = 48 sqrt(7)

Add the area of the bottom:

144 + 48 sqrt(7)

This gives a surface area of 271 square meters (rounded).

To find the height of the pyramid, we can form a right-triangle whose base goes from the center of the 12 by 12 bottom to one of the corners, whose height goes from the center of the 12 by 12 square to the top of the pyramid, and whose hypotenuse is the corresponding edge with measure 8.

This gives the pyramid's height of sqrt(7).

The formula for the volume is:

V = 1/3 * base^2 * height

I get 127 cubic meters (rounded).