Do you want to **calculate the area of a pyramid**? Use our online calculator and we will automatically provide you with data such as the lateral surface area of this figure, the area of its base and the total surface area of this pyramid.

Just enter how long one of the sides of the quadrangular base is and how tall the pyramid is. When you have done this, click the calculate button and we will give you the results.

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**How to calculate the area of a pyramid**

To calculate the area of a pyramid **we have to follow three steps**:

- Remove its lateral surface
- Obtain the area occupied by the quadrangular base.
- Add the results obtained in the two previous points.

Vamos a ver cómo se hace cada uno para que no haya ninguna duda. Presta atención porque dependiendo del tipo de pirámide que tengamos (triangular, cuadrangular, pentagonal, hexágonal...), habrá que usar la fórmula de una forma u otra.

**Lateral area of a pyramid**

The first step in calculating the area of a pyramid consists of **find its lateral surface**. To do so, we will apply the following formula:

Lateral area pyramid = base x height x N / 2

N being the number of sides that the base has. For example, in the case of a triangular pyramid N is 3, in the quadrangular pyramid it will be N= 4, in the pentagonal pyramid N = 5 and so on.

Please note that **the number of sides of the base directly influences the number of faces the pyramid will have**. For example, in the case of a hexagonal pyramid we are talking about 6 faces.

**Base surface**

For** calculating the area of the base of the pyramid** we have to use the formula that corresponds to the polygon at the bottom.

For example, if the base is triangular, the formula is

A = base x height /2

But if the pyramid is quadrangular, we will calculate the area of the base with this other one:

A = side x side

If you need to know the area of any other type of base, leave us a comment and we will help you as soon as possible.

## Exercise solved: quadrangular pyramid

We are asked to **find the area of a quadrangular pyramid** whose height is 12 meters and the side of the base is 4 meters.

Following the steps we have seen in the theory point, the first thing we will do is to take the area of the total surface. Since we are dealing with a **pyramid with square base**the number of sides will be four (N = 4).

Lateral area pyramid = 4 x 12 x 4 / 2 = 96 m

^{2}

Now we calculate the **base area**:

Pyramid base area = 4 x 4 = 16 m

^{2}

**We add** all areas:

Pyramid area = 96m

^{2}+ 16m^{2}= 112 m^{2}

## Example: hexagonal pyramid

Let's look at another practical example but this time we are asked for **find the surface area of a hexagonal pyramid **with a height of 10 meters and whose base sides measure 5 meters.

We put the previous method of resolution into practice again, so the first thing we will do is to calculate the lateral area. In this case** it is a pyramid whose base is a hexagon.** so we have 6 faces:

Lateral area pyramid = 4 x 10 x 6 / 2 = 120 m

^{2}

We found the hexagonal base surface whose formula without to know the apothem es:

Hexagon area = 2.60 - L

^{2}= 2,60 - 5^{2}= 65 m^{2}

We add and obtain the total area of the hexagonal pyramid:

Hexagonal pyramid surface = 120 m

^{2}+ 65 m^{2}= 185 m^{2}

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Draw a regular right quadrangular pyramid of base 6 cm and apothem 8 cm, find height, area and volume.

They assume that all pyramids have a square base.

On the contrary, you have examples to calculate the area of a pyramid whose base can be triangular, quadrangular, pentagonal or even hexagonal. I recommend you to review the content we have to check it ;)

Buena para diseñar y elaborar una pirámide tridimensional que puede descomponerse en dos figuras conocidas. Dibújala y Explica cómo lo harías