Square Pyramid Surface Area
The sides are four triangles with the base edge as their base and the slant height as their height. That slant is the hypotenuse of the height and half the base edge. Four faces plus the base gives the total.
Your numbers
Surface area
360cm²
Slant height
13cm
Lateral area
260cm²
Volume
400cm³
Formula
Slant height = √((Side ÷ 2) ² + Height ²), Surface area = Side ² + 2 × Side × Slant height
Slant height is not the same as edge length. The edge runs to a base corner; the slant runs to the midpoint of a base edge.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| Side (cm)One edge of a square or cube. | 10 | 0 and up |
| Height (cm)The perpendicular height from the base — not the slanted side. | 12 | 0 and up |
Step by step
Quick reference table
Results when only Side (cm) changes and everything else stays put.
| Side (cm) | Surface area (cm²) | Slant height (cm) | Lateral area (cm²) |
|---|---|---|---|
| 5 | 147.58 | 12.258 | 122.58 |
| 7.5 | 244.83 | 12.572 | 188.58 |
| 10 | 360 | 13 | 260 |
| 15 | 649.53 | 14.151 | 424.53 |
| 20 | 1,024.82 | 15.62 | 624.82 |
What each result means
| Result | At default values |
|---|---|
| Surface area (cm²)The total area of a solid’s outer skin. | 360 |
| Slant height (cm)The sloped length from apex to base edge — longer than the height. | 13 |
| Lateral area (cm²)The side surface only, without the bases — the size of a wraparound label. | 260 |
| Volume (cm³)The space a solid holds — length cubed. | 400 |
Common mistakes
Slant height is not the same as edge length. The edge runs to a base corner; the slant runs to the midpoint of a base edge.
Glossary
- Side
- One edge of a square or cube.
- Height
- The perpendicular height from the base — not the slanted side.
- Surface area
- The total area of a solid’s outer skin.
- Slant height
- The sloped length from apex to base edge — longer than the height.
- Lateral area
- The side surface only, without the bases — the size of a wraparound label.
- Volume
- The space a solid holds — length cubed.
Frequently asked questions
Q. How is Square Pyramid Surface Area calculated?
Slant height = √((Side ÷ 2) ² + Height ²), Surface area = Side ² + 2 × Side × Slant height — The sides are four triangles with the base edge as their base and the slant height as their height. That slant is the hypotenuse of the height and half the base edge. Four faces plus the base gives the total.
Q. Can you walk through an example?
With Side 10cm, Height 12cm, the answer is Surface area 360cm².
Q. What do I need to enter?
Enter Side, Height. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only Side (cm) moves the answer to Side (cm) 5 → Surface area (cm²) 147.58 and Side (cm) 20 → Surface area (cm²) 1,024.82. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
Slant height is not the same as edge length. The edge runs to a base corner; the slant runs to the midpoint of a base edge.
Related calculators
Keep your length units consistent across inputs — mixing centimetres and metres throws results far off.