Square Pyramid Surface Area Calculator
Calculate the surface area of a square pyramid by entering the base side length and height. A square pyramid has a square base and triangular faces.
🔺 Square Pyramid Surface Area
Formula
Square Pyramid Surface Area Formulas
Total Surface Area
Includes the square base and 4 triangular faces
Lateral Surface Area
Only the 4 triangular faces, excluding the base
Slant Height
Distance from apex to midpoint of base edge
Volume
Volume of the pyramid
Square Pyramid Surface Area Examples
Example 1: Small Pyramid
Given: Base side = 4 cm, Height = 3 cm
Slant Height: l = √((4/2)² + 3²) = √(4 + 9) = √13 ≈ 3.61 cm
Formula: SA = s² + 2s√((s/2)² + h²)
Solution: SA = 4² + 2×4×3.61 = 16 + 28.84 = 44.84 cm²
Example 2: Medium Pyramid
Given: Base side = 6 cm, Height = 8 cm
Slant Height: l = √((6/2)² + 8²) = √(9 + 64) = √73 ≈ 8.54 cm
Formula: SA = s² + 2s√((s/2)² + h²)
Solution: SA = 6² + 2×6×8.54 = 36 + 102.48 = 138.48 cm²
Example 3: Large Pyramid
Given: Base side = 10 cm, Height = 12 cm
Slant Height: l = √((10/2)² + 12²) = √(25 + 144) = √169 = 13 cm
Formula: SA = s² + 2s√((s/2)² + h²)
Solution: SA = 10² + 2×10×13 = 100 + 260 = 360 cm²
Square Pyramid Surface Area FAQ
What is a square pyramid?
A square pyramid is a 3D shape with a square base and 4 triangular faces that meet at a single point (apex). The Great Pyramid of Giza is a famous example.
What is slant height in a pyramid?
Slant height is the distance from the apex to the midpoint of any base edge, measured along the triangular face surface.
How do you calculate pyramid surface area?
Total surface area uses SA = s² + 2s√((s/2)² + h²), which includes the square base and 4 triangular faces.
What's the difference between height and slant height?
Height (h) is the vertical distance from base to apex. Slant height (l) is the distance along the triangular face from apex to base edge midpoint.