Surface Area of a Pyramid Formula
What is the formula for the surface area of a pyramid?
Answer
Here a is the side (or base), l is the slant height of a face, or the length along the solid. The result comes out in square units.
Where the formula comes from
A square base of a², plus four identical triangular faces. Each face has base a and height l — the slant height of the face — so each is ½·a·l, and four of them give 2·a·l. «Identical» is the load-bearing word: it needs a RIGHT pyramid, whose apex stands over the centre of the square. Lean the apex to one side and the four faces get four different heights, and they have to be added one by one.
Worked examples
Let a = 6, l = 5. Then the surface area of a pyramid = 96 square units.
Let a = 4, l = 3.5. Then the surface area of a pyramid = 44 square units.
The common mistake
Using the pyramid’s own height instead of the slant height of a face. They are different lines: l² = h² + (a/2)². This formula is for a pyramid on a square base; other bases need their own count of faces.
Other quantities: Pyramid
Related Calculations
See Also
- Square Footage Calculator - Width × length in feet to square feet
- Square Feet to Square Meters (Sq Ft to Sq M) - Convert Square Feet to Square Meters
- Square Meters to Square Feet (Sq M to Sq Ft) - Convert Square Meters to Square Feet
- Gravel Calculator - Area to cubic yards, tons and coverage
- Topsoil Calculator - Cubic yards, weight and coverage for any area
- Multiplication Facts - Any two numbers from 1 to 9, with the working shown
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Values from the Formula (l = 5)
| If a = | Surface area |
|---|---|
| 1 | 11 square units |
| 2 | 24 square units |
| 4 | 56 square units |
| 6 | 96 square units |
| 8 | 144 square units |
| 9 | 171 square units |