The Most Elegant Algebraic Formulas

Monday, October 12, 2009
Happy Thanksgiving to everyone!

The most elegant formula to find the total surface area of a cube is TSA=6s². That's basicly saying the length of one side squared, multiplied by 6 (because there are 6 faces on a cube).
Eg.

TSA= 6s²

TSA=6(2²)

TSA=6(4)

TSA=24u²

The most elegant formula to use when finding the TSA of a rectangular prism is
TSA=2(=lw+hl+hw). Luckily you only have to find the area of 3 different sides, thanks to symmetry. When you know one side, you know the opposite side. (Only for Rectangular Prisms)
Eg.
TSA=2(lw+hl+hw)
TSA=2(4x2 + 6x4 + 6x2)
TSA=2(8+24+12)
TSA=2(42)
TSA=84u²

The most elegant formula to find the toal surface area of a cylinder would be TSA=2πr²+2πrh.
2πr² is to find the to circle shaped tops of a cylinder. Then when you add the 2πrh, it's the area of the rectagular net (tube of cylinder). h is the height of the cylinder. 2πr is to find the circumference. (2r x π is equal to πd).
Eg.
TSA=2πr²+2πrh
TSA=2(3.14)(2²)+2(3.14)(2)(10)
TSA=2(3.14)(4)+2(3.14)(2)(10)
TSA=25.12+125.6
TSA=150.72u²

Finally, time for the total surface area of a composite. Sadly, there is no certain formula for TSA's of composite figures. That's only because composite shapes are all different. A composite shape is one big shape made by combining little basic shapes. To find the TSA for these typesof shapes, simply cut the shape into the basic shapes, and then REMEMBER to subtract the area of overlap, from both shapes connecting. (for 3D shapes)

Eg.
O___O What's that shape?....if you think about it, you can turn it into a square and two right angle triangles. Let's give side length of the square 5 and length a (verticle) of the triangle=2.5, with b=6. Usually you would need to find length "c", but since there are two symmetrical triangles it will make a rectangle. So that means you find the area of a square and a rectangle with the dimensions of a triangle.
Area of square= s²
Area of square= 5²
Area of square= 25u²
Area of Rectangle=lw
Area of Rectangle=2.5x6
Area of Rectangle=15u²
TSA=40u²