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A solid oblique pyramid has a regular hexagonal base with an area of 54 cm2 and an edge length of 6 cm. Angle BAC measures 60°. What is the volume of the pyramid?

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Final answer:

To find the volume of an oblique pyramid with a regular hexagonal base, use the formula V = (1/3)Bh. Find the height using trigonometry and substitute the values into the formula.


Step-by-step explanation:

To find the volume of an oblique pyramid, we can use the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid. In this case, the base is a regular hexagon with an area of 54 cm2. We are not given the height of the pyramid, so we need to find it using trigonometry.

Since angle BAC measures 60°, we can see that it is an equilateral triangle. The height of an equilateral triangle can be found using the formula h = (√3/2)a, where a is the length of a side. In this case, the side length is 6 cm, so the height is (√3/2)(6) = 3√3 cm.

Now we can calculate the volume of the pyramid using the formula V = (1/3)Bh. Substituting in the values, we get V = (1/3)(54 cm2)(3√3 cm) ≈ 54√3 cm3.


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