Question

The Rainforest Pyramid at Moody Gardens is a rectangular pyramid that has glass sides to allow the sunlight to enter the building. The base of the building is approximately 320 feet wide and 200 feet long. The height of each side is approximately 140 feet. How many square feet of glass were needed to cover the lateral sides of the pyramid?

Answer 1

We have the following diagram for a rectangular pyramid:

Where:

• h is the height of the pyramid,

,

• s is the slant height, the height of the sides.

The area of the sides (without the base) of the pyramid is given by:

$A=\frac{1}{2}\cdot p\cdot s\text{.}$

Where p is the perimeter of the base.

We have a rectangular pyramid with:

• base with sides a = 320 ft and b = 200 ft,

,

• slant height (heigh of the sides ) s = 140 ft.

The perimeter of the base is:

$p=2\cdot(a+b)=2\cdot(320ft+200ft)=1040ft\text{.}$

Replacing the value of p and s in the formula of the area we get:

$A=\frac{1}{2}\cdot(1040ft)\cdot140ft=72800ft^2.$

Answer

It was needed 72800 ft² of glass.