🔺 Rectangular Pyramid Calculator 2026
Calculate surface area, lateral area, slant heights, and volume
Enter Pyramid Dimensions
l = length, w = width, h = height
📊 Results
Slant Height (l-side)
12.65 cm
Slant Height (w-side)
13 cm
Base Area
80 cm²
Lateral Area
215.2 cm²
Total Surface
295.2 cm²
Volume
320 cm³
📝 Step-by-Step Solution
Given: l = 10 cm, w = 8 cm, h = 12 cm
Slant height (l-side): s₁ = √[h² + (w/2)²] = √[144 + 16] = 12.65 cm
Slant height (w-side): s₂ = √[h² + (l/2)²] = √[144 + 25] = 13 cm
Base Area = l × w = 10 × 8 = 80 cm²
Lateral Area = l×s₁ + w×s₂ = 10×12.65 + 8×13 = 230.5 cm²
Total Surface = Base + Lateral = 80 + 230.5 = 310.5 cm²
Volume = (1/3) × Base × h = (1/3) × 80 × 12 = 320 cm³
📐 Rectangular Pyramid Formulas
Slant Height (along length): s₁ = √[h² + (w/2)²]
Slant Height (along width): s₂ = √[h² + (l/2)²]
Base Area: Abase = l × w
Lateral Area: Alat = l×s₁ + w×s₂
Total Surface: Atotal = lw + l×s₁ + w×s₂
Volume: V = (1/3) × l × w × h
Understanding Rectangular Pyramids
🔺 Shape
Rectangular base + 4 triangular faces meeting at apex. If l = w, it's a square pyramid. Apex is directly above base center in a right pyramid.
📏 Slant Heights
Two different slant heights for rectangular base. s₁ goes to midpoint of length edge. s₂ goes to midpoint of width edge. (Equal if square base.)
📐 Lateral Area
Sum of 4 triangular faces. Two pairs of congruent triangles. Area = (1/2)×base×slant for each. Total: l×s₁ + w×s₂.
📦 Volume
V = (1/3) × Base × Height. One-third of a rectangular prism with same base and height. Works for any pyramid.
Frequently Asked Questions
What is the surface area formula for a rectangular pyramid?
A = lw + l×s₁ + w×s₂. Base area plus four triangular faces. Need
both slant heights for rectangular (non-square) base.
What is the volume formula for a rectangular pyramid?
V = (1/3) × l × w × h. One-third of base area times height. Same
as (1/3) × Base Area × Height.
How do I find the slant height of a rectangular pyramid?
s = √[h² + (half base edge)²]. There are two slant heights: s₁ =
√[h² + (w/2)²] and s₂ = √[h² + (l/2)²].
Why are there two slant heights?
Rectangular base has two different edge lengths. Each slant height
goes from apex to midpoint of an edge. Square pyramids have only one slant height.
What is the lateral surface area?
Alat = l×s₁ + w×s₂. Sum of four triangular faces. Two
triangles with base l, two with base w.
What is the difference between height and slant height?
Height (h): perpendicular from base to apex. Slant
height: along face from apex to edge midpoint. Slant > Height.
How do I find height from slant height?
h = √[s² - (half base)²]. Rearrange Pythagorean theorem. Need to
know which slant height you have.
What if the base is a square?
l = w, so only one slant height. Formulas simplify: Lateral =
2×l×s. Total = l² + 2×l×s. This is a square pyramid.
What is a right rectangular pyramid?
Apex directly above base center. All formulas here assume right
pyramid. Oblique pyramids have apex offset, different formulas.
How do I calculate material for pyramid?
Use total surface area. Includes base if making solid pyramid. Use
lateral area only if making open-bottom pyramid (like tent).
What is the net of a rectangular pyramid?
Rectangle + four triangles attached to edges. When folded,
triangles meet at apex. Used for paper models, sheet metal work.
How does doubling dimensions affect volume?
Volume increases 8×. V = (1/3)lwh, so (2l)(2w)(2h) = 8×(1/3)lwh.
Surface area increases 4×.
What are real-world examples of rectangular pyramids?
Some tents, roof peaks, some buildings, ancient monuments.
Egyptian pyramids are square-based, but concept is similar.
What is the edge length (apex to corner)?
e = √[h² + (l/2)² + (w/2)²]. Distance from apex to any base
corner. All four edges equal in right pyramid.
How do I find the apothem?
Apothem = slant height for pyramids. The perpendicular distance
from apex to a base edge (along the face).
Can base be any rectangle?
Yes, any length and width. Formulas work for all proportions.
Square is special case where l = w.
How accurate is this calculator?
Uses precise mathematical formulas. Assumes right pyramid with
apex over base center. Results are exact.