How to Find the Height of a Rectangular Pyramid

By Bernard Yao; Updated April 24, 2017

Numbers and math are pertinent to the understanding of our world. Some people consider math as a nuisance, while others love the challenge of working with numbers. Knowledge of algebra, a branch of mathematics, will enable you to compute the height of a rectangular-based pyramid. Given the formula for the volume of a rectangular-based pyramid, you can extrapolate that formula to find the height.

Write the formula for the volume of a rectangular-based pyramid. Volume (V) is equal to one third of the base area multiplied by the height (H). Base area is equal to length (L) multiplied by width (W). Therefore, V = 1/3 x (LxWxH).

Extract the formula for the height of a rectangular-based pyramid using your knowledge of algebra. H = V / (L x W) / 3. For instance, V = 60 cubic cm, L = 4 cm and W = 6 cm.

Replace the formula with the given numbers. H = 60 cubic cm / (4 cm x 6 cm) / 3. H = 60 cubic cm / (24 cm squared / 3). H = 60 cubic cm / 8 cm squared. H = 7.5 cm. The height of a rectangular-based pyramid with volume of 60 cubic cm, length of 4 cm and width of 6 cm is 7.5 cm.

Check you answer by completing the formula with the values. V = 1/3 x (L x W x H). 60 cm3 = 1/3 x (4 cm x 6 cm x 7.5 cm). 60 cubic cm = 1/3 x 180 cubic cm. 60 cubic cm = 60 cubic cm and the formula balances out.

About the Author

Bernard Yao began his career as a technical writer and consultant in 2000. His specialties include Web technology, fitness and travel. Yao has traveled throughout the US and 10 other countries. He received a Bachelor of Science in computer science from the University of California, Irvine, where he earned industry certifications from IBM and Sun Microsystems.