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Answer:

19 ft³

Step-by-step explanation:

Volume of the pyramid:

V = 1/3 · B · h

B = 8 ft²

tan 30° = height / 7√3

1/√3 = height / 7√3

height = 7 ft

V =  1/3 · 8 · 7 = 18.67 ft³ ≈ 19 ft³

Answer  ) 19 ft³

The volume of a solid oblique pyramid that has a pentagonal base with base length of 2.16 ft and area of 8 ft² is 19 ft².

Volume of a pyramid

The volume of a pyramid is decribe as follows:

volume of a pyramid = 1 / 3 Bh

where

  • B = base area
  • h = height of the pyramid

Therefore,

B = 8 ft²

h = ?

tan 30° = opposite / adjacent

tan 30° = h / 7√3

h = 7√3 × tan 30°

h = 0.57735026919 × 7√3

h = 6.99575321177

Therefore,

volume = 1 / 3 × 8 × 6.99575321177

volume = 55.9660256942 / 3

volume = 18.6553418981

volume = 19 ft²

learn more on pyramid here: https://brainly.com/question/3008257

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