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# Video:How to Find the Surface Area and Volume of a Isosceles Triangular Prism

with Jonathon Stewart

End your search now - here are formulas and explanations for the surface area and volume of an isosceles triangular prism.See Transcript

## Transcript:How to Find the Surface Area and Volume of a Isosceles Triangular Prism

If you are desperate to uncover the formula for the surface area and the volume of an isosceles triangular prism, you can now breathe a sigh of relief as I've got both of them for you. I know I was up all night worried about these very same formulas not so long ago in my school days last millennium, so I feel your pain. Before busting out the math, let's review some basics in relation to the shape that is an isosceles triangular prism.

### Basics About How to Find the Surface Area and Volume of a Isosceles Triangular Prism

It is a five-sided, or five-faced prism that has an isosceles triangle for its base. The isosceles triangle is a triangle that has two sides of the same length while the third side is different.

### Tips for How toFind the Surface Area and Volume of a Isosceles Triangular Prism

Let's start with the equation for the surface area of an isosceles triangular prism, which will tell us what the total area is of all faces of this shape. The Surface Area equals the base times height (of the triangle) plus double the length of the prism times the length of the non-base side of the triangle plus the length of the prism times the base of the triangle (SA= bh + 2ls + lb).

### Example of How to Find the Surface Area and Volume of a Isosceles Triangular Prism

For example, if the base is 3, height is 4, side is 5 and length is 9 then, base times height is 12; length times side is 45, doubled is 90; and length times base is 27. Add 12, 90 and 27, and you've got the surface area, which is 129. If you're asked for the units, remember that area is always expressed as units squared.

Don't get so lost in the numbers you forget what you're actually doing here, which is simply adding up the areas of the shape of each face. If you're in a pinch and forget the formula, just figure the area for each of the five individual sides, add ‘em, and you're in business. Now, when it comes to volume, remember this is different than surface area because it is concerned with how much space is within the shape rather than on the surface. Imagine filling that isosceles triangular prism up with water. Calculating the volume will tell us just how much water will fit inside. Volume is equal to one-half the base times height times length. (V= ½(bh)l.

Going back to the figures we used before, first, multiply base times height, which is four times three, which equals 12. Half twelve is 6, multiplied by the length of 9, which gives you the volume of 54. If you're asked for the units, remember that volume is expressed as units cubed.Both these equations can be used to determine the area and volume of any size of isosceles triangular prism, just be sure you've got the right numbers in the right places, and plug and chug.

I'm Jonathon Stewart, with About.com.
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