How to calculate the area of the regular pyramid
Do you have to calculate the area of a pyramid and you do not know how to do it? If it is a regular polygon, you only have to apply the formula of the calculation of the lateral area and add the area of the base to find its total base. So do not wait any longer and learn in this article how to calculate the area of the regular pyramid . It's very easy, you'll see!
Steps to follow:one
Suppose we have a cardboard pyramid like the one in the drawing and we propose to calculate the lateral area and the total area of the same.
For that we open the pyramid by one of its edges and unfold it until we get a flat figure. This figure is the development of the pyramid .
two
Note that the development of the pyramid is formed by the triangles that form the lateral area and the base frame. Notice also that the four triangles that make up the lateral area are the same.
Thus:
Lateral area of the pyramid = area of the triangle ABH x 4
In this way, the first step will be to determine the area of each of the triangles that make up the pyramid and then multiply the value by four.
3
But before knowing the total area it will be necessary to find the area of each triangle following the formula:
Area of the triangle = (base x height or apothem) / 2
The lateral area of a regular pyramid is equal to the product of the perimeter of its base by the apothem of the pyramid divided by 2; Remember that the apothem is the height of each of the triangles that form a regular pyramid.
Area of the triangle = (8 x 12) / 2 = 96/2 = 48 cm²
Now that we know the area of each of the triangles, we can now calculate the lateral area of the pyramid, as we explained in the previous step:
Lateral area of the pyramid = area of the triangle ABH x 4 = 48 x 4 = 192 cm²
4
Taking into account that the total area of the pyramid is the sum of the lateral area plus the area of the base, using the measurements of the image of step 1, we can determine that:
Area of the base = 8 cm x 8 cm = 64 cm²
Thus:
Total area of the pyramid = lateral area + area of the base
Total area of the pyramid = 192 + 64 = 256 cm²
