How to find the length of an edge of a polyhedron Flashcards - ACT Math

The volume of a triangular prism can be simply stated as V = A*L, where A is the area of the triangular face and L is the length. We have the volume already and we need to figure out the area of the triangle from the side length.

The area of a triangle is b*h/2, and we are given the base/side length: 3 in. We also have a formula for the height of an equilateral triangle, $b\frac{\sqrt{3}}{2}$ . Calculating the area of the triangle we get 2.5981 in^2, so now we just have to plug our numbers into the volume formula.

$V = A\cdot L\Rightarrow 32 in^3 = 2.5981 in^2 \cdot L$

$L = \frac {32}{2.5981} in = 12.32 in$

And that is the final answer.

How to find the length of an edge of a polyhedron - ACT Math

If we have a regular (the triangles are equilateral) triangular prism of volume and the side length of the triangle on either face is , what is the length of the prism? Write your answer in terms of a decimal rounded to the nearest hundredth.