Most Elegant Algebraic Expressions

Hello everyone! I'm sorry I couldn't go on for a few days, my Internet wasn't working properly. Finally it's working. So now I can do the posts Mr. Backe assigned us. And I can finally comment too. So anyways I am going to tell you the Most Elegant ways to find Rectangular Prisms, Triangular Prisms, the Cube, the Cylinder, and any Square Based Prism.

The Rectangular Prism:

SA=2(lw)+2(hl)+2(hw)

SA=2(6)(10)+2(4)(10)+2(4)(6)

SA=120+80+48

SA=248 square units

The Triangular Prisms:

First you find the area of a triangle.

A=bh/2

A=(4)(4)/2

A=16/b

A=8 square units

And then the base.

A=bh

A=(4)(10)

A=40 square units

And finally the roofs.

You have to find the hypotenuse by using the Pythagorean Theorem.

a squared + b squared = c squared

4 squared + 4 squared = c squared

16 + 16 = c squared

32 (square rooted) = c squared (square rooted)

5.656 = c

A=2[h(Hyp.)]

A=2[10(5.656)]

A=2(56.56)

A=113.12 square units

Then you add all of the answers together.

113.12 + 40 + 8 = 161.12 square units

I know it looks complicated but this is as elegant it's gonna get.

The Cube:

SA= 6s squared

SA= 6(3) squared

SA= 6(9)

SA= 54 units square

The Cylinder:

SA=2 pi r squared + 2 pi r h

SA=2(3.14)(3)squared + 2 (3.14)(3)(8)

SA=2(3.14)(9) + 2(3.14)(24)

SA=(3.14)18+ (3.14) 48

SA=56.52+150.72

SA=207.24

Any Square Based Prism:

You could use this if you have any Prism with a square. You could use it as a base. If you had a rectangular prism with a square on the sides than you use this formula.

Thank you for reading! Please leave a comment and tell me how I did!