To find the volume of a pyramid we must use the equation

 $\displaystyle Volume\: of\: pyramid=\frac{1}{3}(area\ of\ base)(height)$

We must first solve for the area of the square using

$\displaystyle A=(side\ length^{2})$

We plug in $\displaystyle 7$ and square it to get $\displaystyle A=49$

We then plug our answer into the equation for the pyramid with the height to get

 $\displaystyle V=\frac{1}{3}(49)(15)$

We multiply the result to get our final answer for the volume of the pyramid

 $\displaystyle V=245$.

The formula for the volume of a pyramid is:

$\displaystyle V = \frac{wlh}{3}$

where $\displaystyle w$ is the width of the base, $\displaystyle l$ is the length of the base, and $\displaystyle h$ is the height of the pyramid.

In order to determine the height of the pyramid, you will need to use the Pythagoream Theorem to find the slant height:

$\displaystyle A^2 + B^2 = C^2$

$\displaystyle A^2 + (5m)^2 = (13m)^2$

$\displaystyle A^2 = 144m^2$

$\displaystyle A = 12m$

Now we can use the slant height to find the pyramid height, once again using the Pythagoream Theorem:

$\displaystyle A^2 + B^2 = C^2$

$\displaystyle A^2 + (5m)^2 = (12m)^2$

$\displaystyle A^2 = 119m^2$

$\displaystyle A = \sqrt{119}m$

Plugging in our values, we get:

$\displaystyle V = \frac{wlh}{3}$

$\displaystyle V = \frac{(10m)(10m)(\sqrt{119}m)}{3}$

$\displaystyle V = \frac{100\sqrt{119}m^3}{3} \approx 364m^3$

The formula for the volume of a pyramid is:

$\displaystyle V = \frac{1}{3} (base)(height)$

$\displaystyle V = \frac{1}{3} (l)(w)(h)$

Where $\displaystyle l$ is the length of the base, $\displaystyle w$ is the width of the base, and $\displaystyle h$ is the height of the pyramid

Use the Pythagorean Theorem to find the length of the slant height:

$\displaystyle A^2 + B^2 = C^2$

$\displaystyle A^2 + (6m)^2 = (10m)^2$

$\displaystyle A = 8m$

Now, use the Pythagorean Theorem again to find the length of the height:

$\displaystyle A^2 + B^2 = C^2$

$\displaystyle A^2 + (6m)^2 = (8m)^2$

$\displaystyle A = 2\sqrt{7}m$

Plugging in our values, we get:

$\displaystyle V = \frac{1}{3} (12m)(12m)(2\sqrt{7}m)$

$\displaystyle V = 96\sqrt{7}m^3$

A square pyramid has one square base and four triangular sides.

Vertices (where two or more edges come together):  5. There are four vertices on the base (one at each corner of the square) and a fifth at the top of the pyramid.

Edges (where two faces come together):  8. There are four edges on the base (one along each side) and four more along the sides of the triangular faces extending from the corners of the base to the top vertex.

Faces (planar surfaces):  5. The base is one face, and there are four triangular faces that form the top of the pyramid.

Total $\displaystyle = 5 + 8 + 5 = 18$

Volume of Pyramid = 1/3 * Area of Base * Height

12,000 ft³ = 1/3 * 30ft * 30ft * H

12,000  = 300 * H

H = 12,000  / 300 = 40

H = 40 ft

Volume of a pyramid is

$\displaystyle \frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (height)$

Thus:

$\displaystyle 8=\frac{1}{3}\cdot (Area\ of\ the\ base)\cdot (6)$

$\displaystyle 8=2\cdot (Area\ of\ the\ base)$

Area of the base is $\displaystyle 4\ ft^{2}$.

Therefore, each side is $\displaystyle 2\ ft$.

To find the surface area of a pyramid we must add the areas of all five of the shapes creating the pyramid together.

We have four triangles that all have the same area and a square that supports the pyramid.

To find the area of the square we take the side length of 15 and square it $\displaystyle 15^{2}=225$

The area of the square is  $\displaystyle 225$.

To find the area of the triangle we must use the equation for the area of a triangle which is $\displaystyle \frac{base\times height}{2}$

Plug in the slant height 12 as the height of the triangle and use the side length of the square 15 as the base in our equation to get

 $\displaystyle \frac{1}{2}*15*12=90$

The area of each triangle is $\displaystyle 90$.

We then multiply the area of each triangle by 4 to find the area of all four triangles $\displaystyle 4*90=360$.

The four triangles have a surface area of $\displaystyle 360$.

We add the surface area of the four triangles with the area of the square to get the answer for the surface area of the pyramid which is $\displaystyle 360+225=585$.

The answer is  $\displaystyle 585$.

The formula for the surface area of a pyramid is:

$\displaystyle SA = 4 \left(A_{triangle}\right)+Base$

$\displaystyle SA = 4 \left(\frac{1}{2}{h_{s}}w\right)+(lw)$

Where $\displaystyle h_s$ is the length of the slant height, $\displaystyle w$ is the width of the base, and $\displaystyle l$ is the length of the base

In order to determine the areas of the triangle, you will need to use the Pythagorean Theorem to find the slant height:

$\displaystyle A^2 + B^2 = C^2$

$\displaystyle A^2 + (5m)^2 = (13m)^2$

$\displaystyle A^2 = 144m^2$

$\displaystyle A = 12m$

Plugging in our values, we get:

$\displaystyle SA = 4 \left(\frac{1}{2}\cdot (12m)(10m)\right)+((10m)(10m))$

$\displaystyle SA = 240m^2+100m^2 = 340m^2$

The formula for the surface area of a pyramid is:

$\displaystyle SA = (base)+\frac{1}{2}(perimeter)(slant height)$

$\displaystyle SA = (l)(w) + \frac{1}{2}(l+l+w+w)(h_s)$

Where $\displaystyle l$ is the length of the base, $\displaystyle w$ is the width of the base, and $\displaystyle h_s$ is the slant height

Use the Pythagorean Theorem to find the length of the slant height:

$\displaystyle A^2 + B^2 = C^2$

$\displaystyle A^2 + (6m)^2 = (10m)^2$

$\displaystyle A = 8m$

Plugging in our values, we get:

$\displaystyle SA = (12m)(12m) + \frac{1}{2}(12m+12m+12m+12m)(8m)$

$\displaystyle SA = 336m^2$

The surface area of of a square pyramid can be determined using the following equation:

$\displaystyle SA=2bs+b^2$

$\displaystyle SA=(2)(6)(4)+4^2$

$\displaystyle SA=48+16=64$