Question

Find a formula for the volume in terms of x

Answer 1

one thing to note is that, for a triangular prism, its volume is the area of the triangular face times its length. Keeping in mind the triangle there, has a base of 2x + 1, and a height of x.

`\bf \left[ \stackrel{\textit{area of the triangle}}{\cfrac{1}{2}\stackrel{base}{(2x+1)}\stackrel{height}{(x)}} \right]~~\stackrel{\textit{length of the prism}}{(x+8)}\implies \cfrac{2x^2+x}{2}(x+8)\\\\\\\cfrac{2x^3+x^2+16x^2+8x}{2}\implies \cfrac{2x^3+17x^2+8x}{2}\implies \stackrel{\textit{distributing the denominator}}{x^3+\cfrac{17}{2}x^2+4x}`

Answer 2

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