# Surface Area of a Rectangular Pyramid Calculator

Use this surface area of a rectangular pyramid calculator to deal with rectangular pyramids. Whether rectangular or square, these kinds of pyramids are famously associated with history across the globe! Be it the **Egyptian pyramids** or the Latin American ones. Pyramids are not just monuments but are also useful in determining the hardness of materials! The **Vickers hardness test** uses a **pyramid indenter** for that purpose. This article will explain how you can calculate its surface area.

## Surface area of a rectangular pyramid

The total surface area of a rectangular pyramid ($A_t$) is the sum of two areas:

- The area of the base; and
- The area 4 surrounding triangles, otherwise known as the lateral surface area.

Consider a rectangular pyramid with the following dimensions:

- a - Base
**length**; - b -
**Width**of the base; and - h -
**Height**of the pyramid.

Now, the area of the base ($A_b$) is a rather simple calculation. It is the area of a rectangle, i.e.

Whereas, you can calculate the **lateral surface area** as an **area of a triangle**. If the slant heights are $l_a$ and $l_b$, for the respective sides, the lateral surface area is given by the equation:

You can write the **slant heights** in the form of height and base length of the pyramid. Such that the lateral surface area becomes:

## Example: Using the surface area of rectangular pyramid calculator.

Find the surface area of a rectangular pyramid having base dimensions as `4`

and `5 cm`

. Take the height of the pyramid as `5 cm`

.

To find the surface area:

**Enter**the**length**of the base as`5 cm`

.**Insert**the**width**of the base as`4 cm`

.- Fill in the
**height**of the pyramid as`5 cm`

. - The
**surface area**of a rectangular pyramid calculator will return the area as:

**Advanced mode**

You can enable the `advanced`

mode to view the slant height and face areas of the pyramids.

## Other rectangular pyramid calculators

There are other tools based on rectangular pyramids that you can refer to learn more cool things about this omnipresent shape, such as:

## FAQ

### How do I calculate the slant height of the rectangular pyramid?

To calculate the slant height of the rectangular pyramid:

- Find the
**square**of the**base length of the pyramid**. **Divide**the square by`4`

.**Add**the resultant with the**square of the height of the pyramid**.- Find the
**square root**of the sum to obtain the slant height of the pyramid. **Repeat**the steps with the**base width**to find the other slant height.

### How do I calculate the lateral surface area of a rectangular pyramid?

To calculate the lateral surface area of a rectangular pyramid:

- Find the
**slant heights**of the pyramid. **Multiply****slant height**with the**base length**of the pyramid.**Repeat step 2**with the**base width**.**Add**the two**areas**to obtain the lateral surface area of the pyramid.

### What is the surface area of a pyramid with base length 4 cm and height 6 cm?

The surface area of the pyramid is `66.6 sq. cm`

. Out of which, the `50.6 sq. cm`

is the lateral surface area, which is calculated as: `2 × 4 × √((0.25×16) + 36) = 50.6 sq. cm`

., while `16 sq. cm`

is the base area.