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Rectangular prisms are six-sided polygons; three-dimensional shapes of which all sides meet at 90-degree angles, like a box. Cubes are a special type of rectangular prism of which all sides are the same length; this is the key difference between cubes and other rectangular prisms. Understanding this difference can make finding out other things about these shapes — like how to measure their volumes and surface areas — quite simple.
Dimensions
Rectangular prisms — cubes included — have three dimensions: length, width and height. Sit a prism on a flat surface and take a look at it. Facing the prism, a side that runs back to front is the length, a side that runs from left to right is the width and a side that runs up and down is the height.
Identification
Like a square, all sides of a cube are the exact same length, which means its length, width and height are all equal. Rectangular prisms that aren’t cubes can have any two of these dimensions the same (which makes it a “square prism”) or all three can be different. These shapes fall into a category called “cuboids.” Until you become familiar with their main characteristics, the best way to tell these two polygons apart is to compare their sides.
Calculating Surface Area
The surface area of a polygon is the total area of all of the flat faces of the shape. The basic formula to find the surface area of a cuboid (including rectangular prisms and cubes) is:
Surface Area = 2xlength + 2xwidth + 2xheight, or shorthand, A=2L+2W+2H
Since a cube has the same measurement for length, width and height, the surface area can be found through a shortcut; just make the first calculation (2L, for example) and multiply that by 3; or six times the length of any side.
Calculating Volume
The volume of a polygon is the amount of space inside the shape. Think of volume like this: How much water would this polygon hold if you filled it to the brim? The formula to find the volume for all cuboids is:
Volume = Length x Width x Height, or V=LWH
A similar shortcut exists for finding the volume of a cube. Multiply the measurement of the cube’s sides to the power of three, or “cube” it. For example, if the sides of a cube each measure 3 inches, calculate 3^3=27 cubic inches.
