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=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(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).

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=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

## 2 comments:

Nice job Joseph! Very understandable. Great examples, but I think you should add "a little" more colour (; And awesome pictures, too! Great post!

Nice post Joseph! (: I like your examples.

## Post a Comment