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

Surface Area: SA = s² + 2s√((s/2)² + h²)
Slant Height: l = √((s/2)² + h²)
Where s is the base side length and h is the height

Square Pyramid Surface Area Formulas

Total Surface Area

SA = s² + 2s√((s/2)² + h²)

Includes the square base and 4 triangular faces

Lateral Surface Area

LSA = 2s√((s/2)² + h²)

Only the 4 triangular faces, excluding the base

Slant Height

l = √((s/2)² + h²)

Distance from apex to midpoint of base edge

Volume

V = (1/3)s²h

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.