Right Rectangular Pyramid Calculator
Calculate volume, surface area, lateral area, and base area of a right rectangular pyramid
Calculate Pyramid Properties
Length of the rectangular base
Width of the rectangular base
Perpendicular height from base to apex
Pyramid Properties
Example Calculation
Pyramid Example
Base Length (a): 6 inches
Base Width (b): 8 inches
Height (H): 12 inches
Calculations
Base Area: 6 × 8 = 48 in²
Volume: (48 × 12) ÷ 3 = 192 in³
Base Diagonal: √(6² + 8²) = 10 in
Lateral Edge: √(12² + 5²) = 13 in
Pyramid Components
Base Length
Length of rectangular base
One side of the rectangle
Base Width
Width of rectangular base
Other side of the rectangle
Height
Perpendicular distance to apex
From base center to top
Formula Reference
Understanding Right Rectangular Pyramids
What is a Right Rectangular Pyramid?
A right rectangular pyramid is a three-dimensional solid with a rectangular base and four triangular faces that meet at a single point (apex) directly above the center of the base. The "right" designation means the apex is positioned directly over the center of the base.
Key Components
- •Rectangular base: Base with length (a) and width (b)
- •Four triangular faces: Two pairs of congruent triangles
- •Height (H): Perpendicular distance from base to apex
- •Lateral edges: Lines from base corners to apex
Pyramid Formulas Explained
Volume Formula
V = (base_area × height) ÷ 3
Volume is one-third the base area times the height. This is a fundamental property of all pyramids, regardless of base shape.
Surface Area Formula
A = A_b + A_l
Total surface area is the sum of the base area (A_b) and the lateral surface area (A_l), which includes all four triangular faces.
Lateral Calculations
Uses Pythagorean theorem
Slant heights and lateral edge calculations use the Pythagorean theorem with the pyramid height and base dimensions.
Real-World Applications
Architecture & Construction
- • Pyramid-shaped buildings and monuments
- • Roof design and calculations
- • Structural engineering applications
- • Material quantity estimation
Manufacturing & Design
- • Packaging design optimization
- • Product design calculations
- • Volume and material planning
- • Geometric modeling
Education & Research
- • Geometry education and training
- • Mathematics problem solving
- • 3D visualization studies
- • Engineering calculations
Historical Context: The Great Pyramid
Great Pyramid of Giza
The Great Pyramid of Giza is one of the most famous examples of pyramid geometry in the real world. With a square base (essentially a rectangular pyramid where length equals width), it demonstrates the practical application of pyramid calculations.
- Base side length: ~230 meters (440 Egyptian Royal cubits)
- Original height: ~147 meters (280 Egyptian Royal cubits)
- Volume: Approximately 2.59 million cubic meters
Volume Calculation Example
Given: Base = 230m × 230m, Height = 147m
Base Area: 230 × 230 = 52,900 m²
Volume: (52,900 × 147) ÷ 3 = 2,592,100 m³
This massive volume demonstrates the scale of ancient engineering achievements!