# How to find the surface of a prism

## What is a prism

A prism is a polyhedron, which is a solid object made up of two congruent (similar and equal-sized) polygonal faces whose identical edges are connected by rectangles. The polygonal area is called the base of the prism, and the two bases are parallel to each other. However, it is not necessary that they are positioned exactly one above the other. If they are exactly on top of each other, if the rectangular sides and the base meet at right angles, then the prism is called a right-angled prism.

Each of these shapes can be called a prism.

## How to find the surface of a prism: method

A prism contains at least 5 faces. Also, if the prism is irregular, it is likely that the area of ​​each area will need to be calculated separately and added to get the total area. However, with a regular prism of known geometry, this problem is a little easier.

Prism has two bases and n rectangles that connect these surfaces. In some cases the shape is irregular and the area varies from one surface to another. Then we can find the area of ​​the prism using the following formula.

Total area = 2 [area of ​​the base] + [area of ​​all sides, the rectangles]

If the bases are a regular polygon, the sides or rectangles will be similar and the same size. Therefore, it is enough to calculate the area of ​​a single base and the area of ​​a single rectangle. Assuming a regular prism geometry and an n- sided polygon as the basis, the total area results.

Total area = 2 [area of ​​the base] + n [area of ​​one side, the rectangle]

Triangular prisms are the most common type of prism, and if we consider an equilateral triangular prism with, we can change the above formula to:

Total area of ​​a triangular prism = 2 [1/2 ah] +3 [al]

Where the length of one side of the prism is l , h is the vertical height of the triangle with side a .

## How to find the surface of a prism: Example

1. A prism has a cross-sectional area of ​​an equilateral triangle with a side length of 3 cm. When the prism is four inches long, determine the total area of ​​the prism.
• Find the area of ​​the base

The base is an equilateral triangle with 3cm. Hence the area of ​​the triangle

• Find the area of ​​one side.

One side has a rectangular shape and a length of 10 cm and a width of 3 cm, hence the area of ​​a single page,

• There are 3 sides and two bases in a triangular prism, so the total area of ​​the prism is