# pyramid....

• Jan 24th 2010, 05:42 PM
orochimaru700
pyramid....
1.) Find the lateral area of a regular hexagonal pyramid if each edge of base is 10m and each lateral edge is 15m.

2.) Find the volume and the lateral area of a regular triangular pyramid if the altitude is 20 inches and the base of equal sides is 9 inches.

3.) Find the volume and the total area of a triangular pyramid if each lateral edge is 30 meters and the base is 10 meters on a side. It's base is an equilateral triangle.
• Jan 25th 2010, 05:05 PM
Soroban
Hello, orochimaru700!

Here's the first one . . .

Quote:

1) Find the lateral area of a regular hexagonal pyramid
. . .if each edge of base is 10m and each lateral edge is 15m.

I assume the "lateral edge" is what most of us call the "slant height".

One of the triangular side panels looks like this:
Code:

              *             /|\             / | \           /  |  \ 15           /  h|  \         /    |    \         /    |    \       /      |      \       * - - - * - - - *                   5

From Pythagorus: .$\displaystyle h^2 + 5^2 \:=\:15^2 \quad\Rightarrow\quad h^2 \:=\:200 \quad\Rightarrow\quad h \:=\:10\sqrt{2}$

The area of this triangle is: .$\displaystyle \tfrac{1}{2}bh \:=\:\tfrac{1}{2}(10)\left(10\sqrt{2}\right) \:=\:50\sqrt{2}\text6{ m}^2$

Therefore, the area of the six panels is: .$\displaystyle A \;=\;6\times 50\sqrt{2} \;=\;300\sqrt{2}\text{ m}^2$