Surface Area of a Rectangular Pyramid Calculator

Calculate the total surface area of a rectangular pyramid. Enter base length, width, and pyramid height to find slant heights, lateral face areas, and total SA.

Enter Pyramid Dimensions

Result

Total Surface Area
0
square units

Step-by-Step Solution

Surface Area of a Rectangular Pyramid

A rectangular pyramid has a rectangular base and four triangular faces that meet at a single apex above the base. The total surface area is the sum of the base area and the areas of all four triangular faces.

Key Formulas

Base Area

The rectangular base area is simply length times width.

A_base = l x w

Slant Height (length side)

The slant height of the triangular face along the length side.

s_l = sqrt(h^2 + (w/2)^2)

Slant Height (width side)

The slant height of the triangular face along the width side.

s_w = sqrt(h^2 + (l/2)^2)

Total Surface Area

Sum of the base area and all four lateral triangular faces.

SA = lw + l x s_l + w x s_w

How It Works

The apex of the pyramid is directly above the center of the rectangular base. Each triangular face has a base equal to one side of the rectangle and a slant height measured from the midpoint of that base edge to the apex. The two faces along the length have slant height s_l, and the two faces along the width have slant height s_w.

Applications

  • Architecture: Pyramid-shaped roofs, atriums, and decorative structures.
  • Packaging: Calculating material for pyramid-shaped boxes or containers.
  • History: Understanding the geometry of ancient pyramids.
  • Engineering: Material estimation for pyramid-shaped components.