Surface Area of a Rectangular Pyramid Calculator

Surface Area of a Rectangular Pyramid

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

$$A_t = A_b + A_l$$

where $A_b = a \times b$ is the base area, and $A_l = a \cdot l_a + b \cdot l_b$ is the lateral area. The slant heights are:

$$l_a = \sqrt{h^2 + \left(\frac{b}{2}\right)^2}, \quad l_b = \sqrt{h^2 + \left(\frac{a}{2}\right)^2}$$

Example

For a pyramid with base 6 cm by 4 cm and height 7 cm:

$$A_b = 6 \times 4 = 24 \text{ cm}^2$$

Frequently Asked Questions

What is the difference between height and slant height?

Height is the perpendicular distance from the apex to the base. Slant height is the distance from the apex to the midpoint of a base edge along a triangular face.

How many faces does a rectangular pyramid have?

It has five faces: one rectangular base and four triangular lateral faces.

Why are there two different slant heights?

When the base is a rectangle (not a square), the two pairs of opposite triangular faces have different slant heights because the base sides have different lengths.

What units should I use?

Use the same linear unit for base length, base width, and height. The surface area will be in square units of that measurement.

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Surface Area of a Rectangular Pyramid Calculator