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Lesson 4: 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).
• Wish me luck on this test guys, Tomorrow is a big day and I can't seem to understand, any tips, I am being a bit hesitant because I have dementia on stuff like this. Thanks!
• 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
• what is a triangle