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Area and volume SAT question

Math · Geometry and Trigonometry · Medium · Answer it here, explanation included.

A triangular prism has a height of and a volume of . What is the area, , of the base of the prism? (The volume of a triangular prism is equal to , where is the area of the base and is the height of the prism.)

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ExplanationShow

The correct answer is . It's given that a triangular prism has a volume of and the volume of a triangular prism is equal to , where is the area of the base and is the height of the prism. Therefore, . It's also given that the triangular prism has a height of . Therefore, . Substituting for in the equation  yields . Dividing both sides of this equation by yields . Therefore, the area, , of the base of the prism is .

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