Frustum of a Pyramid

The frustum of a pyramid or truncated pyramid is the result of cutting a pyramid by a plane parallel to the base and separating the part containing the apex.

Truncated Pyramid

The lateral faces of a pyramidal frustum are trapezoids.

The height of the pyramidal frustum is the perpendicular distance between the bases.

The apothem is the height of any of its sides.

Unfold of a Pyramidal Frustum

Unfold of a Truncated Pyramid

Apothem of a Pyramidal Frustum

Apothem of a Truncated Pyramid

To calculate the apothem of a pyramidal frustum, the height, the apothem of the biggest base and the apothem of the minor base must be known. Apply the Pythagorean theorem to determine the length of the hypotenuse of the shaded triangle to obtain the apothem:

Apothem of a Truncated Pyramid Formula

Apothem of a Truncated Pyramid Formula

Area and Volume of a Pyramidal Frustum

Area and Volume of a Truncated Pyramid

Area and Volume of the Truncated Pyramid

Area and Volume of the Truncated Pyramid

Area and Volume of the Truncated Pyramid

Area and Volume of the Truncated Pyramid

Area and Volume of the Truncated Pyramid

Area and Volume of the Truncated Pyramid

Area and Volume of the Truncated Pyramid

Area and Volume of the Truncated Pyramid

Example

Calculate the lateral area, surface area and volume of the truncated square pyramid whose larger base edge is 24, smaller base edge is 14 cm and whose lateral edge is 13 cm.

tronco de pirámide cuadrangular

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