First, you will want to create a pyramid with measurements that are easy to calculate. So, let's say that we have pyramid with a base edge of 10 inches and a height of 10 inches. 

So the volume of the original pyramid would be equal to 

$\displaystyle \frac{(10\times 10)(10)}{3}=\frac{1000}{3}=333.33\: inches^2$

The volume of the altered pyramid would be equal to:

$\displaystyle \frac{(7\times 7)(12)}{3}=\frac{588}{3}=196\: inches^2$

To find the relationship between the volume of the altered pyramid relative to the volume of the original pyramid, divide the altered volume by the original volume. 

$\displaystyle \frac{196}{333.33}=.59$

The new volume is 59% of the original volume, which means there was a 41% decrease in volume. 

If the length of one side is 756 ft, then multiply to find the area of the base.

$\displaystyle \text{Area of square} = \text{length} \times \text{width}$

$\displaystyle A=756\times756$

$\displaystyle A=571,536 ft^{2}$

Once you've found the area of the base, use the height of the pyramid and half of the side length of the base to determine the length of the side from the apex to the ground using the Pythagorean Theorem. 

$\displaystyle 480^{2}+378^{2}=c^{2}$

$\displaystyle 230,400+142,884=c^{2}$

$\displaystyle 373,284=c^{2}$

$\displaystyle 611=c$

Using the side length of the base and the height of each of the triangles that form the pyramid, calculate the area of each triangle, then multiply by 4.

$\displaystyle \text{Area of a triangle}=\frac{1}{2}\times \text{base} \times \text{height}$

$\displaystyle A=\frac{1}{2} \times 611 \times 756$

$\displaystyle A=230,958$

$\displaystyle \text{Area of four triangles} = 4 \times 230,958$

$\displaystyle A=923,832 ft^{2}$

Add the surface area of the base to the surface area of the four triangles.

$\displaystyle \text{Total surface area} = 571,536 + 923,832$

$\displaystyle 1,495,368 ft^{2}$

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 $\displaystyle 2\ ft$.

If the height, which is twice the length of the base edges, measures 6 meters, then each base edge must measure 3 meters.  

Since the base is a square, the area of the base is 3 x 3 = 9.  

Therefore the volume of the right pyramid is V = (1/3) x area of the base x height = 1/3(9)(6) = 18.

The formula for the area of a pyramid is $\displaystyle \frac{lwh}{3}$. In this case, the length is $\displaystyle 8$, the width is $\displaystyle 6$, and the height is $\displaystyle 9$. 

$\displaystyle 8\times6\times9=432$ and $\displaystyle 439\div3=144$. 

To find the volume of a pyramid, you need to use the equation below:

$\displaystyle Volume=\frac{(area\, of\, the\, base)(height)}{3}$

To find the height (shown by the yellow line), we can draw a right triangle using the yellow line, blue line and side b (5 inches). Because the hypotenuse is 5 inches, using the common Pythagorean 3-4-5  triple. The blue line is 3 inches and the yellow line (height) is 4 inches. Also, to find side a, we can use the blue line (3 inches) and half of the red line (3 inches)  and the Pythagorean Theorum.

$\displaystyle 3^2+3^2=(side\, a)^2$

$\displaystyle 9+9=(side\, a)^2$

$\displaystyle 18=(side\, a)^2$

$\displaystyle \sqrt{18}\, in=side\, a$

Because the base is a square, the area of the base is equal to the square of side a:

$\displaystyle (side a)^2=18\: in^2$

Now we plug in these values to find the volume:

$\displaystyle Volume=\frac{(18)(4)}{3}$

$\displaystyle Volume=\frac{(72)}{3}$

$\displaystyle Volume=24\, in^3$

The volume $\displaystyle V$ of a rectangular pyramid with height $\displaystyle h$, base width $\displaystyle w$, and base length $\displaystyle l$ is given by 

$\displaystyle V=\frac{1}{3}lwh$.

For this pyramid, $\displaystyle h=4in.$, $\displaystyle w=6in.$, and $\displaystyle l=6in.$ To calculate its volume, substitute the values for $\displaystyle h$, $\displaystyle w$, and $\displaystyle l$ into the formula:

$\displaystyle V=\frac{1}{3}(6)(6)(4)=\frac{144}{3}=48$

Therefore, the volume of the given rectangular pyramid is $\displaystyle 48in.^3$