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

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Find The Length Of An Edge Of A Polyhedron

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.

Possible Answers:

Not enough information to decide.

Correct answer:

Explanation:

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, . 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.

And that is the final answer.

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