### Elegant Algebraic Expressions

Monday, October 12, 2009
First of all.. I'd like to say HAPPY THANKSGIVING/TURKEY DAY to everyone! (: Okay so this blog post will be about the most elegant algebraic expressions to help you find the surface area for a cube, a rectangular prism, a cylinder, and a composite shape. So let's start! :D

What is the most elegant algebraic expression for
a cube?
The most elegant algebraic expression for a cube is 6s².

So now, we'll use a 2 by 2 cube for an example to find the surface area.

This is how you find the surface area for a cube: S.A. of cube = 6s
²
S.A. of cube = 6(2²)
S.A. of cube = 6(4)
S.A. of cube = 24u
²

What is the most elegant algebraic expression for a rectangular prism?
The most elegant algebraic expression for a rectangular prism is 2(lw)+2(hw)+2(lw).

For an example, we'll use a rectangular prism with a length of 5, a width of8, and a height of4.

This is how you find the surface area for a rectangular prism:
S.A. of rectangular prism =
2(lw)+2(hw)+2(lw)
S.A. of rectangular prism =
2(5x8)+2(4x8)+2(5x8)
S.A. of rectangular prism = 2(40)+2(32)+2(40)

S.A. of rectangular prism = 80+64+80

S.A. of rectangular prism = 224cm
²

What is the most elegant algebraic expression for a cylinder?
The most elegant algebraic expression for a cylinder is 2
πr²+2πrh.

To show how to find the surface area of a cylinder, we'll use a cylinder with a diameter of 10 and a height of 15.

This is how you find the surface area for a cylinder:
d/2 = r
10/2 = r
5 = r

S.A. of cylinder =
2πr²+2πrh
S.A. of cylinder = 2π5²+2π5(15)
S.A. of cylinder = 2π25+2π75
S.A. of cylinder = 50π+150π
S.A. of cylinder = 157.079+471.238
S.A. of cylinder = 628.317u²

What is a composite figure?
A composite figure is a figure or shape that can be divided into more than one of the basic figures.

Here is an example of a composite figure:
This figure is divided into two squares and triangles, which are basic shapes.

How does symmetry help us solve some of these surface area problems?
Symmetry helps us solve these surface area problems because if you know a shape has symmetry you would that it is balanced. Like a rectangle.. it's front is the same as it's back, and so as the 2 sides and the top and bottom. I'm not sure if I made sense here though.

OKAY.. So I hope this blog post helped anyone who needed help! If there's anything missing, or if there's any errors, don't be afraid to comment~! Have a good Thanksgiving/Turkey Day you guys and I'll see you tomorrow~!