Case 1
- Base edge b (square base)
- 6
- Slant height l (up a face, not vertical)
- 5
96.00
Open with these valuesPyramid Surface Area Calculator
96.00units²
Result: 96.00 units²A square pyramid is one square base plus four identical triangles: A = b² + 2 × b × l. With a base edge of 6 and a slant height of 5 that is 36 + 60 = 96 square units. The slant height runs up the middle of a face — it is not the vertical height of the pyramid.
The numbers at a glance
Held fixed: Base edge b (square base) 6.000.
| Slant height l (up a face, not vertical) | Result |
|---|---|
| 2.000 | 60.00 |
| 4.000 | 84.00 |
| 5.000Your value | 96.00 |
| 6.000 | 108.00 |
| 8.000 | 132.00 |
| 10.000 | 156.00 |
Worked examples
Case 2
- Base edge b (square base)
- 1
- Slant height l (up a face, not vertical)
- 1
3.00
Open with these valuesCase 3
- Base edge b (square base)
- 10
- Slant height l (up a face, not vertical)
- 8
260.00
Open with these valuesHow it's calculated
A = b² + 2 × b × l
- StepMeasure one side of the square base.
- StepMeasure up the middle of a triangular face to the apex.
- ResultSquare the base edge and add twice base edge times slant height.
Reference table
| Base edge, slant height | Lateral surface | Base + lateral | Total surface |
|---|---|---|---|
| 0.5, 2 | 2 | 0.25 + 2 | 2.25 |
| 1, 1 | 2 | 1 + 2 | 3 |
| 2, 3 | 12 | 4 + 12 | 16 |
| 4, 4.5 | 36 | 16 + 36 | 52 |
| 6, 5 | 60 | 36 + 60 | 96 |
| 10, 8 | 160 | 100 + 160 | 260 |
Questions
How do I calculate the surface area of a pyramid?
For a square pyramid, add the base area to the four triangular faces: A = b² + 2 × b × l, with b the base edge and l the slant height. With b = 6 and l = 5 that is 36 + 60 = 96 square units.
What is the slant height of a pyramid?
It is the distance from the middle of a base edge straight up the centre of a triangular face to the apex, the face apothem. It is not the vertical height of the pyramid. Surface area uses it because each face is a triangle whose height is that slant.
What is the difference between lateral and total surface area?
The lateral surface is only the four triangles, 2 × b × l — the part you would paint or clad. The total adds the square base b² on top. Use the lateral figure when the base sits on the ground and is never seen.
I only know the vertical height — how do I find the slant height?
For a right square pyramid the slant height is √(h² + (b ÷ 2)²), where h is the vertical height and b the base edge. Work that out first, then enter it here.
Which units does the answer use?
Whatever you entered, squared. Base edge and slant height in centimetres give square centimetres, in inches square inches. Both inputs must use the same unit.
Sources and last check
Information, not professional advice.