a prism has 2 congruent hexagonal bases like the one shown. each hexagon is made from 2 congruent isosceles trapezoids.

the volume of the prism is 234 cubic units. what is the height of the prism?

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8 units

Question

a prism has 2 congruent hexagonal bases like the one shown. each hexagon is made from 2 congruent isosceles trapezoids.

the volume of the prism is 234 cubic units. what is the height of the prism?

3 units
4 units
6 units
8 units

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Isosceles Trapezoid Properties" ], "new_concepts": [ "Volume of a Prism", "Area of a Hexagonal Base" ], "current_concepts": [ "Isosceles Trapezoid Properties", "Volume of a Prism", "Area of a Hexagonal Base" ] } ## Calculate the area of one isosceles trapezoid $$ \begin{aligned} b_1 &= 5 \ b_2 &= 4 + 4 = 8 \ h &= 3 \ A_{\text{trapezoid}} &= \frac{1}{2} (b_1 + b_2) h \ A_{\text{trapezoid}} &= \frac{1}{2} (5 + 8) \times 3 = 19.5 \end{aligned} $$ ## Calculate the total base area of the hexagonal base $$ \begin{aligned} B &= 2 \times A_{\text{trapezoid}} \ B &= 2 \times 19.5 = 39 \end{aligned} $$ ## Solve for the height of the prism $$ \begin{aligned} V &= B \times H \ 234 &= 39 \times H \ H &= \frac{234}{39} = 6 \end{aligned} $$

3 units

4 units

6 units

8 units

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Volume of a Prism" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the area of one isosceles trapezoid

Calculate the total base area of the hexagonal base

Solve for the height of the prism

Answer: