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The volume of a rectangular prism is 6x3 + 19x2 + 2x - 3

and the height is x + 3. What is the area of the base of the prism?

User Jjankowiak
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1 Answer

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To find the area of the base of the rectangular prism, we need to find the expression for the area of a rectangle with dimensions equal to the dimensions of the base of the prism.

The volume of a rectangular prism is given by the formula:

Volume = length * width * height

Substituting the given expressions for the volume and the height into this formula, we get:

6x3 + 19x2 + 2x - 3 = (length * width) * (x + 3)

Expanding the right-hand side of the equation, we get:

6x3 + 19x2 + 2x - 3 = length * width * x + length * width * 3

Matching the terms on the left-hand side of the equation with the corresponding terms on the right-hand side, we can see that the expression for the area of the base of the rectangular prism is:

length * width = 6x3 + 19x2 + 2x - 3 - length * width * 3

Simplifying this expression, we get:

length * width = -3x3 - 17x2 - 2x + 3

Therefore, the area of the base of the rectangular prism is given by the expression -3x3 - 17x2 - 2x + 3.

User WildThing
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