determine the volume of a right rectangular pyramid with the base dimensions 6 ft by 12 ft. For each triangular face, the equal sides have length 18 ft. Write answer to nearest cubic ft.

Consider the cross section perpendicular to the base through opposite corners of the base. It will be an isosceles triangle with legs of 18 ft and a base dimension equal to the diagonal of the base rectangle.

That diagonal length is given by the Pythagorean theorem as ...

d² = 6² +12² = 180

d = √180 = 6√5

Then the right triangle that tells us the height of the pyramid has a base length of (1/2)(6√5) and a hypotenuse of 18. The pyramid height is ...

(3√5)² + h² = 18²

h = √(324 -45) = √279 = 3√31

So, the volume of the pyramid is ...

V = (1/3)Bh

V = (1/3)((6 ft)(12 ft))(3√31 ft) = 72√31 ft³ ≈ 401 ft³

janlee113 janlee113 · Answer 2 · 2021-07-06T18:43:26+02:00

janlee113 janlee113

06-07-2021

Answer:

401 ft³

Explanation:

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determine the volume of a right rectangular pyramid with the base dimensions 6 ft by 12 ft. For each triangular face, the equal sides have length 18 ft.​ Write answer to nearest cubic ft.​

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401 ft³

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determine the volume of a right rectangular pyramid with the base dimensions 6 ft by 12 ft. For each triangular face, the equal sides have length 18 ft. Write answer to nearest cubic ft.