### Elegant Algebraic Expressions

Sunday, October 18, 2009
Hello everyone! I am making this blog post to show you the most elegant algebraic expressions for the surface area of a cube, rectangular prism, and a cylinder. I will also be answering some questions.

SURFACE AREA OF A CUBE = 6s²

S.A. = 6s²
S.A. = 6(2²)
S.A. = 6(2x2)
S.A. = 6(4)
S.A. = 24u²

SURFACE AREA OF A RECTANGLE = 2(lw)+2(lh)+2(hw)

S.A. = 2(lw)+2(lh)+2(hw)
S.A. = 2(5x6)+2(5x4)+2(6x4)
S.A. = 2(30)+2(20)+2(24)
S.A. = 60+40+48
S.A. = 148cm²

SURFACE AREA OF A CYLINDER = 2πr²+2πrh

S.A. = 2πr²+2πrh
S.A. = 2π(4²)+2π(4)h
S.A. = 2π(4x4)+2π(4)h
S.A. = 2π(16)+2π(4)
S.A. = 32π+8π
S.A. = 100.48+25.12
S.A. = 125.6cm²

COMPOSITE SHAPES
- a composite shape is a shape that can be divided into basic shapes, like a square, a rectangle, a triangle, etc.

This figure can be divided into two basic shapes, a triangle and a square.

HOW DOES SYMMETRY HELP US SOLVE SOME OF THESE SURFACE AREA PROBLEMS?
It helps us solve some of these area problems because some of the shapes have symmetry. Some shapes have sides that are the same, like, a square. all 6 sides have identical sides. If we know that there it has identical sides, then we can form a formula to solve the surface area of the shape.

WHAT HAPPENS IF A PART OF ANY OF THESE SHAPES IS MISSING? HOW DO I FIND SURFACE AREA THEN?
If there was a part missing in any of these shapes, you would have to calculate the missing area, and subtract it from the original shape.

THANK YOU FOR READING MY BLOG POST ! (: I hope this helps you learn more about surface area and please feel free to comment if I made any mistakes.