Surface Area of a Pyramid in Square Feet Calculator
Get precise measurements for your pyramid’s surface area with our advanced calculator.
Input Measurements
Pyramid Type
Results
Total Surface Area:
— ft²
Base Surface Area:
— ft²
Lateral Surface Area:
— ft²
Calculation Details
3D Visualization
Visualization will appear here after calculation
Understanding Pyramid Surface Area
Square Pyramid Formulas
Total Surface Area: SA = a² + 2a√(a²/4 + h²)
Base Surface Area: BA = a²
Lateral Surface Area: LSA = 2a√(a²/4 + h²)
Where a = side length of base, h = height of pyramid
Rectangular Pyramid Formulas
Total Surface Area: SA = lw + l√(w²/4 + h²) + w√(l²/4 + h²)
Base Surface Area: BA = l × w
Lateral Surface Area: LSA = l√(w²/4 + h²) + w√(l²/4 + h²)
Where l = length, w = width, h = height of pyramid
Triangular Pyramid Formulas
Total Surface Area: SA = base area + lateral surface area
Base Surface Area: BA = (1/2) × base × base height
Lateral Surface Area: Sum of the areas of all triangular faces
Requires calculating the area of each triangular face separately
Applications & Examples
Real-World Applications
- Calculating material needed for pyramid-shaped roofs
- Determining paint required for pyramidal structures
- Engineering calculations for pyramid-shaped monuments
- Architecture and construction planning
- Educational purposes in teaching geometry
Example Calculation
Problem: Find the surface area of a square pyramid with base side length 10 feet and height 12 feet.
Step 1: Calculate the base area: BA = 10² = 100 ft²
Step 2: Calculate slant height: s = √(12² + 5²) = √(144 + 25) = √169 = 13 ft
Step 3: Calculate lateral surface area: LSA = 2 × 10 × 13 = 260 ft²
Step 4: Calculate total surface area: SA = 100 + 260 = 360 ft²
Frequently Asked Questions
What is the surface area of a pyramid?
The surface area of a pyramid is the sum of the area of its base and the area of all its triangular faces (lateral surface area).
How do you calculate the slant height of a pyramid?
For a square pyramid, the slant height (s) can be calculated using the Pythagorean theorem: s = √(h² + (a/2)²), where h is the height and a is the side length of the base.
What’s the difference between lateral and total surface area?
The lateral surface area includes only the triangular faces of the pyramid, while the total surface area includes both the base and all triangular faces.
Can this calculator handle different types of pyramids?
Yes, this calculator can determine the surface area for square-based, rectangular-based, and triangular-based pyramids.
What units does this calculator use?
This calculator uses square feet (ft²) for all surface area measurements, but the principles apply to any unit of measurement.
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