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## Geometry for Beginners – How To Find the Surface Area and Volume of Prisms

Welcome to Geometry for Beginners. In this article, we’ll start looking at the three-dimensional equivalents of the two-dimensional relationships of perimeter and area. The perimeter of polygons refers to “the distance around” while the area of polygons refers to “the space inside”. For three-dimensional figures, such as prisms, “distance around” becomes area; and “inner space” becomes volume. We will introduce the formulas for finding both the surface area and volume of prisms and discuss the applications of these concepts.

Before we discuss the formulas, we need to make sure that we are all representing the same type of figure. We use a cereal box for our mental image. Our cereal box is an example of a **right rectangular prism**. *RIGHT* because the sides (*side faces*) are perpendicular to the top and bottom (*bases*). *RECTANGULAR* because the *bases* (above and below) are *rectangles*. PRISM because the figure has two identical polygonal bases parallel to each other and 4 lateral faces that are rectangles.

Note: If the sides were not perpendicular to the bases, the figure would be OBLIQUE, not right, and the lateral faces would be parallelograms instead of rectangles. An oblique triangular prism would have the sides NOT perpendicular to the bases, the bases would be triangles, and the 3 lateral faces would be parallelograms.

Again, imagining our cereal box, the surface would refer to the packaging or the box itself. For packaging manufacturers, the amount of material required for each box is extremely important. The cereal inside the box would represent the volume of the package, assuming the box is full. This is an equally important business concern.

The surface area and volume formulas will look unusual because they use symbols we haven’t used before, but only the symbols are new. You already have the skills to use these formulas!

**Formula for the surface of the prisms: SA = 2B + LA**where *SA is the surface area*, *B is AREA from the base*i

*LA is the lateral area*.

Thus, to calculate the surface area of a prism, we must first calculate B, the area of any polygon that forms the base, using the appropriate formula for the shape. This value must then be multiplied by two since there are 2 bases.

Next, we need to calculate the lateral area which is the sum of the areas of the sides. Since the sides are rectangles or parallelograms, we will use the formula A = bh. Then add the sides for the side area. Attention! Make sure you use the actual height and not a side if the sides are parallelograms.

The final step is to add your values of 2B and LA.

The best way to memorize and read the formula SA = 2B + LA is **“The surface area of a prism is equal to twice the area of the base plus the sum of the areas of all the lateral sides.”** Remember that area is always labeled as square units.

**Formula for the volume of prisms: V = Bh**where again *B is the* * AREA from the base* i

*h is the height*of the prism

Attention! Remember that the edge of the prism is the height **only if** the figure is a right prism. If the prism is oblique, the height will have to be calculated as required in non-right triangles.

The formula V = Bh should be read as** “The volume of a prism is equal to the area of the base times the height of the prism.”** Note that volume is labeled as cubic units.

I think you can say that these formulas are actually quite simple to calculate **YES** you have mastered the terminology and area formulas of two-dimensional polygons. The secret to success in geometry: **Memorize! Memorize! Memorize!**

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