Volume
96.00
Base Area
36.00
Surface Area
138.53
Perpendicular height from base to apex
96.00
cubic units
V = (1/3) × 36.00 × 8.00
36.00
square units
102.53
sum of all triangular faces
138.53
base area + lateral area
V = (1/3) × Base Area × hThe volume of any pyramid is one-third the product of the base area and the perpendicular height.
Where:
Base Area= Area of the polygonal base (s² for square, l×w for rectangular, (√3/4)s² for equilateral triangle)h= Perpendicular height from base to apexl = √(h² + (s/2)²)The slant height is the distance from the midpoint of a base edge to the apex.
Where:
h= Perpendicular height from base to apexs= Side length of the square basel= Slant height of each triangular faceSA = s² + 2slTotal surface area is the square base plus four triangular lateral faces.
Where:
s= Side length of the square basel= Slant heights²= Area of the square base2sl= Lateral area (4 triangular faces)Inputs
Result
Base area = 6² = 36. Volume = (1/3)(36)(8) = 96. Slant = √(64 + 9) = √73 ≈ 8.54. Lateral SA = 2(6)(8.54) = 102.53. Total SA = 36 + 102.53 = 138.53.
Inputs
Result
Base area = 4 × 6 = 24. Volume = (1/3)(24)(10) = 80. Slant along length faces = √(100 + 9) = 10.44. Slant along width faces = √(100 + 4) = 10.20. Lateral = 4(10.44) + 6(10.20) = 102.96. Total SA = 24 + 102.96 = 126.96.
Volume = (1/3) × base area × height. For a square pyramid with base side 6 and height 8: V = (1/3) × 36 × 8 = 96 cubic units. The formula works for any base shape.
| Base Type | Dimensions | Height | Volume |
|---|---|---|---|
| Square | 6 × 6 | 8 | 96.00 |
| Square | 10 × 10 | 12 | 400.00 |
| Rectangular | 4 × 6 | 10 | 80.00 |
| Triangular | side 6 | 8 | 41.57 |
For a square pyramid, slant height l = √(h² + (s/2)²), where h is the vertical height and s is the base side length. For base 6 and height 8: l = √(64 + 9) = √73 = 8.54.
| Base Side | Height | Slant Height |
|---|---|---|
| 4 | 6 | 6.32 |
| 6 | 8 | 8.54 |
| 8 | 10 | 10.77 |
| 10 | 12 | 13.00 |
Total SA = base² + 2 × base × slant height. For base 6 and slant height 8.54: SA = 36 + 2 × 6 × 8.54 = 36 + 102.53 = 138.53 square units.
A square pyramid has a square base (all sides equal), while a rectangular pyramid has a rectangular base (length ≠ width). The square pyramid has identical triangular faces on all 4 sides.
A pyramid is a polyhedron with a polygonal base and triangular faces that meet at a common point called the apex. The most common types are square, rectangular, and triangular pyramids.
The volume of any pyramid is exactly one-third the volume of a prism with the same base and height. This relationship was proven by ancient Greek mathematicians.
Pyramid calculations are used in architecture, construction (hip roofs), packaging (carton design), and archaeology (studying ancient monuments like the Egyptian pyramids).
Last Updated: Mar 9, 2026
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