Activity #$1$: Pyramid area $-$ team

In engineering and science, we often want to calculate the effect of some complex behavior. To make

this possible, we create a model of the behavior. A model attempts to describe the behavior in a way

that is understandable and computable. Some models are based on physical laws and principles, some

are based on replicating observations, and many are a combination of these. Once you have a model,

you can use it to analyze and predict the performance or behavior of some system or phenomenon. In

this activity, your team will need to develop a model to calculate a requested quantity of interest.

An ancient ruler has decided to build a Geometry Temple in the form of a square$-$base pyramid made up

of cubes with a given side $($as illustrated below$).$ The Temple has $n$ layers, where the bottom layer is

$nn$ meters and the top layer is a single cube. The ancient ruler wants the surface of the Temple to be

covered with gold. What is the total area of gold foil that is needed in order to accomplish this?

Your team has decided to help the ancient ruler. Your team needs to develop a model to calculate the

total area of gold foil that will cover the Temple $($that is$,$ to cover the visible side and top surface areas,

not the bottom and hidden areas$).$

Lab: Topic $6($team$)$

Write a program named pyramid$\_$area$1.$py that will ask the user to input the length of one side of a

cube $($in meters$)$ and the number of layers of the pyramid. Your program must use a loop. After you

complete this program, write a second program named pyramid$\_$area$2.$py that performs the same

calculation $-$ but this time without a loop $($hint: arithmetic progression$).$ Your programs may NOT use

lists, tuples, or dictionaries.

Remember to test your code. The ancient ruler would not be happy if the ancient builders ran out of

gold foil before the Temple was covered completely. The ruler would get even more upset if the ancient

builders asked for more gold than was needed. Have your program format the output as shown below.

The area should be displayed using two $(2)$ decimal places.

Example output $($using inputs $1,5)$:

Enter the side length in meters: $1$

Enter the number of layers: $5$

You need $85\mathrm{.}00$ m$^2$ of gold foil to cover the pyramid

Note: Both programs should yield the same output!