Rectangular Pyramid Calculator

Enter the base length, base width, and height into the calculator to determine the volume and lateral surface area of the rectangular pyramid.

Rectangular Pyramid

From Volume

Frustum

Units Base Preset (sets Width from Length) Base Length (m) Base Width (m) Height (m) Volume (m³) Lateral Surface Area (m²) Total Surface Area (m²) Slant Height (faces with base = Length) (m) Slant Height (faces with base = Width) (m)

Units Base Preset (sets Width from Length) Base Length (m) Base Width (m) Volume (m³) Height (m) Lateral Surface Area (m²) Total Surface Area (m²) Slant Height (faces with base = Length) (m) Slant Height (faces with base = Width) (m)

Units Top Base Preset (sets Top from Bottom) Bottom Base Length L₁ (m) Bottom Base Width W₁ (m) Top Base Length L₂ (m) Top Base Width W₂ (m) Height (m) Volume (m³) Lateral Surface Area (m²) Total Surface Area (m²) Slant Height (faces with base lengths L₁/L₂) (m) Slant Height (faces with base widths W₁/W₂) (m)

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Rectangular Pyramid Formula

The following equations are used to calculate the volume and lateral surface area of a rectangular pyramid.

Volume Formula:

V = (l * w * h) / 3

Where V is the volume of the pyramid
l is the base length
w is the base width
h is the height

Multiply the base dimensions and height, then divide the product by 3 to calculate the volume.

Lateral Surface Area Formula:

LSA = l * sqrt((w/2)^2 + h^2) + w * sqrt((l/2)^2 + h^2)

Where LSA is the lateral surface area of the pyramid
l is the base length
w is the base width
h is the height
sqrt denotes the square root function

Calculate the lateral surface area by finding the slant heights for the pyramid’s faces and summing the areas of the corresponding triangles.

What is a Rectangular Pyramid?

Definition:

A rectangular pyramid is a three-dimensional geometric shape with a rectangular base and triangular faces that converge to an apex above the center of the base. It is commonly found in architecture and used in various mathematical applications.

How to Calculate the Dimensions of a Rectangular Pyramid?

Example Problem:

The following example outlines the steps needed to calculate the volume and lateral surface area of a rectangular pyramid.

First, consider a pyramid with a base length of 10 units, a base width of 8 units, and a height of 6 units.

Next, calculate the volume using the formula above:

V = (10 * 8 * 6) / 3

V = 480 / 3

V = 160 units³

Then, calculate the lateral surface area using the formula:

LSA = 10 * sqrt((8/2)^2 + 6^2) + 8 * sqrt((10/2)^2 + 6^2)

LSA ≈ 10 * sqrt(52) + 8 * sqrt(61)

LSA ≈ 72.1111 + 62.4816

LSA ≈ 134.5927 units²

FAQ

What are the practical applications of a rectangular pyramid?

Rectangular pyramids are often used in architectural designs, art installations, and engineering projects, as well as in educational geometry problems.

Why is the volume of a pyramid one-third that of a prism with the same base and height?

This one‑third factor results from the pyramid’s tapering shape, which causes it to occupy only one‑third of the space of a prism with an identical base area and height.

Can I use this calculator for pyramids with non‑rectangular bases?

This calculator is specifically designed for rectangular pyramids; different formulas are needed for pyramids with other base shapes.