什么是表面积？

Let's imagine that we're beading a plains tribe style moccasin. We need to find out how much buckskin we'll need to make a size nine ladies moccasin.

Let's imagine that we draw the template of a moccasin on graph paper. The number of squares inside of the moccasin's outline, is the area of the moccasin.

A picture of a moccasin

After doing this exercise, we can see that a size nine ladies moccasin takes up 100 squares of graph paper. Therefore, if each square is 1/4 inches squared, a moccasin would require 40 square inches of buckskin. Therefore, the area of the moccasin template is 40 square inches.

Surface area is the total area of all the external faces of a solid.

Now for some formulas

Surface area of a cube: $6s^2$ in which $s$ is the side length of the cube.

Surface area of a rectangular prism: $2(lw+lh+hw)$ in which $l,w,h$ are the length, width and height of the prism, respectively.

Surface area of a Sphere:$\frac{4r^3 \pi }{3}$ in which $r$ is the radius of the sphere.

Surface are of a tetrahedron:$\sqrt{3}s^2$ in which $s$ is the side length of the tetrahedron

Surface area of a pyramid: $B + \frac{PL}{2}$ in which $B$ is the area of the base, $P$ is the perimeter of the base, and $L$ is the slant height.

Surface are of a cone: $\pi r \left(\sqrt{r^2+h^2}\right)+2\pi r^2$ in which $r$ is the radius of the base and $h$ is the height of the cone.