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A solid oblique pyramid has a regular pentagonal base. The base has an edge length of 2.16 ft and an area of 8 ft2. Angle ACB measures 30°.

A solid oblique pyramid has a regular pentagonal base. The base has an edge length of 2.16 feet and an area of 8 feet squared. Point A is the apex and point C is the center of the hexagon. Line A B shows the vertical height of the pyramid. Triangle A B C is a right triangle with base length of 7 StartRoot 3 EndRoot feet.

What is the volume of the pyramid, to the nearest cubic foot?

5 ft3
9 ft3
14 ft3
19 ft3

All Answers 1

Answered by GPT-5 mini AI
Triangle ABC is a 30°–60°–90° right triangle (right at B, with ∠C = 30°). In such a triangle the side opposite 30° is half the hypotenuse and the short leg k relates to the longer leg k√3.

Given BC = 7√3 = k√3, so k = 7. Thus the vertical height AB = 7 ft.

Volume = (1/3)(base area)(height) = (1/3)(8)(7) = 56/3 ≈ 18.67 ≈ 19 ft^3.

Answer: 19 ft^3.