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Lesson 5: Nets of 3D figures

# Surface area using a net: rectangular prism

A polyhedron is a three-dimensional shape that has flat surfaces and straight edges.  Learn whether or not a certain net could be folded up into a certain rectangular prism. Created by Sal Khan.

## Want to join the conversation?

• Is there a way to find the surface area without using a net? Isn't there a formula for doing this?
• Any prism is given by SA = PH +2B where P is the perimeter of the base (in a rectangular prism, you could choose any side as one of the bases), H is the height of the prism (the third dimension apart from the length and width of the base) and B is the area of the base. So if you can find the base (it could be a triangle, rectangle, parallelogram, etc.) and can calculate the area and perimeter, you can find the surface area. Cylinders work also, but C is used in the place of P and is 2 π r and B = π r^2, so S = 2π r H + 2π r^2 = 2 π r(H + r).
• how do you find the surface area of a hexagon
• Interesting question!

2-D figures, such as a hexagon, have area, not really surface area. 3-D figures have surface area.

A hexagon with side length s can be divided into 6 non-overlapping equilateral triangles with side length s.

An equilateral triangle with side length s can be divided into two right triangles, each with one leg s/2 and hypotenuse s, such that the legs with lengths s/2 together form the base of the equilateral triangle. It follows from the Pythagorean theorem that the leg common to both right triangles (the altitude of the equilateral triangle) is s*sqrt(3)/2. So the equilateral triangle's area is (1/2)s*s*sqrt(3)/2 = s^2*sqrt(3)/4.

So the area of a hexagon with side length s is 6s^2*sqrt(3)/4 = 3s^2*sqrt(3)/2.
• What is a formula? Can anyone give me an example? 🤔
• A formula is a way to express a relationship in math, for example the formula to convert from inches to feet is 1/12 * number of inches. In geometry, most formulas will probably look more like 2𝜋r, the formula to get the diameter of a circle given the radius, or base * height / 2, the formula to get the area of a right triangle. I hope this helps! You can learn anything!
• what does surface area mean?
• Surface area is how many cubic units make up the surface.
Say a cube, for instance.
Take one face, and say it's 3 by 6.
The surface area of that one face would be 18 cubic units.
• So what is a POLYHEDRON?
• It's a 3-dimensional figure with multiple FLAT faces and NO curved surfaces. It's basically the 3D version of a polygon. An example of a polyhedron is a cube, while a cylinder is not a polyhedron (since it has curved faces).
• what if you do not have the little hash marks on the net?
• Check for reference, its not gonna be the same area im pretty sure
• Why did people decide to use hash marks to show same lengths?
• They use it so you can see which ones are similar its also easy to know
• i have an question why do you have to shade it in and what is surface area mean
(1 vote)
• To answer your first question, I think he does it so it is easier for us to understand what part he is talking about.

To answer your second question, the surface area is basically all the areas of each face combined.