### Most Elegant Algebraic Expressions

Friday, October 16, 2009
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

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.

Mr. B. said...

Great job! Really liked your diagrams and explanations

angela905 said...

Good job Zerlina! Nice pictures, and explanations! :D

melanie905 said...

Awesome job Zerlina! Nice colours and pictures. Your examples are very clear and understandable. Keep it up!

Lissa 9-05 said...

Great post! I like your images they were easy to see and read. I also like how you used colours (: