How to get the area of a prism

Prisms are geometric figures with polygonal faces and bases, which can be regular or irregular. To calculate the area of ​​the prisms, you will first need to calculate their perimeter, that is, the sum of their sides. If you need to calculate the lateral or total area of ​​one of these polyhedral, be sure to consult this article to learn how to find the area of ​​a prism.

Steps to follow:

1. Suppose we have a straight prism made of cardboard and we open it until it is fully extended. The figure that we obtain when opening the prism is called the development of the prism. Observe it and you will see that it is formed by the lateral faces and the bases of the prism.

When developing the prism, its lateral faces are transformed into the rectangle ABCD. Therefore, the lateral area of ​​the prism is equal to the area of ​​the rectangle ABCD.

Rectangle base = 6 cm + 2 cm + 6 cm + 2 cm = 16 cm.

Height of the rectangle = 10 cm.

Then:

Lateral area of ​​the prism = 16 cm x 10 cm = 160 cm².

Notice that 6 cm + 2 cm + 6 cm + 2 cm = 16 cm is the perimeter of the base of the prism and that 10 cm is the height of the prism.

2. From the previous section, we can affirm that:

Side area of ​​prism = perimeter of base x height

This formula allows you to calculate the lateral area of ​​any prism. To find the total area, we must add the area of ​​the bases to the lateral area. Since the bases are the same, we can say:

Total area of ​​the prism = lateral area + 2 x base area.

3. We are going to calculate the lateral area and the total area of ​​the prism whose dimensions are indicated in the drawing. The area of ​​the base is in this case:

6 cm x 2 cm = 12 cm²

Thus:

Total area of ​​the prism = 160 cm² + 2 x 12 cm² = 184 cm²

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