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The volume of a solid is the three‑dimensional space it occupies, which can also be viewed as the capacity for holding a fluid or gas. For a square‑based pyramid—think of an Egyptian pyramid—you can determine this volume using a straightforward formula that requires only the pyramid’s height and the length of one side of its base.
Use V = A × h/3, where V is the volume, A is the base area, and h is the perpendicular height from the apex to the base’s center.
Measure or calculate the pyramid’s height and the length of one side of its base. For example, a pyramid with a 5‑inch base side and a 6‑inch height. Ensure all measurements use the same unit. The height must be the perpendicular distance from the apex to the base’s midpoint—not the slant height along a face.
If you’re only given the slant height, treat it as the hypotenuse of a right triangle whose legs are the pyramid’s height and half the base side. Apply the Pythagorean theorem:
a² + b² = c²
where c is the slant height, a is half the base side, and b is the required height.
Square the base side to find the area: 5 in × 5 in = 25 in².
Multiply the base area by the height, then divide by three:
25 in² × 6 in = 150 in³
150 in³ ÷ 3 = 50 in³
Thus, the pyramid’s volume is 50 cubic inches.
For a rectangular base, first compute the base area by multiplying its length and width. For instance, a 5‑inch by 4‑inch base yields an area of 20 in². The remaining steps—multiplying by height and dividing by three—remain identical.
Follow this method to accurately determine the volume of any square or rectangular‑based pyramid without advanced calculus.
