Prisms are geometric figures that are characterized for having two equal bases and lateral faces called parallelograms. Knowing how to calculate the area of a prism is key and essential to solve applications in the field of mathematics, geometry or even in everyday life.
In the next article we are going to tell you How and how is the area of a prism calculated? and we are going to show you a series of examples so that the explanation is easier and simpler to understand.
What is meant by a prism
Before delving into calculating the area of a prism, it is important to know and understand its structure. A prism is a geometric figure that consists of two identical bases and side faces that are parallelograms. The bases can be of any shape, whether squares, rectangles or triangles.
General calculation of the area of a prism
When calculating the area of a prism you must know, on the one hand, the area of the two bases and the area of their lateral faces. The two areas are then added to calculate the total area of the prism. In this way it can be said that the general formula for the area of a prism is the following:
- Prism area: 2 x area of the base + area of the side faces
- To calculate the area of the lateral faces, It is necessary to know the height of the prism and the perimeter of the base.
- Then you multiply the height times the perimeter of the base.
How to calculate the area of a rectangular prism
The rectangular prism is the most common and common prism. In this prism the base is a rectangle and the side faces are also rectangles. If you want to calculate its area you must follow the following steps:
- First of all you have to measure the length, width and height of the rectangular prism.
- Secondly You have to calculate the area of the base, To do this you have to multiply the length by the width of the prism.
- Next you must calculate the areas of the lateral faces: 2 x (length + width) x the height of the prism.
- Finally, you must obtain the total area of the rectangular prism: 2 x area of the base plus the area of the side faces.
Practical example of calculating the area of a rectangular prism
Let's give you an example so that it is clear to you. How to find the total area of a prism with a rectangular base:
- The rectangular prism has the following measurements: length (6 cm), width (4 cm) and height (8 cm).
- Area of the base of the rectangular prism would be the following: 6 x 4 = 24 cm.
- Area of the lateral faces would be calculated as follows: 2 x (6+4) x 8=2 x 10 x 8 = 160 square centimeters.
- Total area of the rectangular prism would be: 2 x 24 +160 = 48 +160 = 208 square centimeters.
In this way the total area of the rectangular prism It would be about 208 square centimeters.
How to calculate the area of a triangular prism
A triangular prism It has bases in the shape of triangles and the lateral faces that are parallelograms. To calculate the area of a triangular prism you must follow the following steps:
- First of all you must measure the length of the sides of the base and the height of the prism.
- Secondly, we must calculate the area of the base: ½ x base x height.
- Next you have to calculate the area of the lateral faces: perimeter of the base of the prism x height.
- Finally, the total area of the triangular prism would be the following: 2 x area of the base + area of the side faces.
Example of how to calculate the area of a triangular prism
The triangular prism has the following measurements: sides of the triangular base (5cm, 12cm and 13cm) and the height about 10 cm.
- First of all we must calculate the area of the base of the triangular prism: (½) x 5 x10 = 25 square centimeters.
- Secondly, we must calculate the perimeter of the base triangle: 5 + 12 + 13 = 30 centimeters.
- The next thing is to calculate the area of the lateral faces: 30 x 10 = 300 square centimeters.
- Finally, it remains to calculate the total area of the triangular prism: 2 x 25 + 300 = 50 + 300 = 350 square centimeters.
In this way the total area of the triangular prism It would be about 350 square centimeters.
In short, calculating the area of a prism is key when it comes to knowing its total surface area. Regardless of whether your base is triangular, rectangular or hexagonal, the general process to find out the total area is to calculate the area of the bases and the area of the lateral faces and add it all up. The formula to calculate the area is not that complicated and is easy to do, so you will not have excessive problems when calculating it. Knowing the area of a prism is often essential in the field of mathematics, architecture and even in daily life.