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.
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.
Let's see how to do each one so that there is no doubt. Pay attention because depending on the type of pyramid we have (triangular, quadrangular, pentagonal, hexagonal...), we will have to use the formula in one way or another.
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.
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 basethe number of sides will be four (N = 4).
Lateral area pyramid = 4 x 12 x 4 / 2 = 96 m2
Now we calculate the base area:
Pyramid base area = 4 x 4 = 16 m2
We add all areas:
Pyramid area = 96m2 + 16m2 = 112 m2
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 m2
Hexagon area = 2.60 - L2 = 2,60 - 52 = 65 m2
We add and obtain the total area of the hexagonal pyramid:
Hexagonal pyramid surface = 120 m2 + 65 m2 = 185 m2