Pyramid volume: identify the base and perpendicular height

What the formula really asks for

Pyramid volume is one third of the product of the base area and the perpendicular height. The height must be measured at right angles to the chosen base. A sloping edge looks tempting in a sketch, but it is usually longer than the true height and will inflate the answer.

Worked example with numbers

A square-based pyramid has base side 6 cm and perpendicular height 5 cm. Base area = 6 × 6 = 36 cm². Volume = (1/3) × 36 × 5 = 60 cm³. Write the conclusion: the volume of the pyramid is 60 cm³.

Second check

Suppose the base area is instead 48 cm² and the height is 9 cm. Then V = (1/3) × 48 × 9 = 144 cm³. If your answer is about three times the corresponding prism volume, you forgot the factor 1/3.

Exam habit

Label the base, mark a right angle for the height, and keep the unit cm³. If the question gives a lateral edge instead of the perpendicular height, construct a right triangle first and find the true height before substituting.

Worked example

Practice questions

1. Find the volume when the base area is 75 cm² and the perpendicular height is 8 cm.
2. A square-based pyramid has side 10 cm and height 12 cm. Find its volume.
3. Explain in one sentence why a lateral edge cannot always replace the height.

Study notes