Surface Area of a Prism

A prism is a three-dimensional (3D) geometric shape with straight, parallel sides. It can be either triangular, rectangular, or square in shape. A prism is named based on the shape of its base. For example, a triangular prism has a triangular base, and a rectangular prism has a rectangular base. The surface area of a prism is the total area of all its faces. To find the surface area of a prism, we need to know the surface area of each individual face and then add them all together. In this blog post, we will explore how to find the surface area of a prism. We will start with the basics and then move on to more complicated formulas. By the end of this post, you should have a good understanding of how to find the surface area of any prism!

What is a Prism?

A prism is a three-dimensional figure with two parallel, identical faces (bases) and rectangular sides. The bases are typically parallelograms, but they can be any polygon.

What is the Formula for Surface Area of a Prism?

A prism is a three-dimensional geometric shape with two identical ends and flat sides. The surface area of a prism can be calculated using the formula:

Surface Area = 2(lw + wh + lh)

where l is the length of the prism, w is the width, and h is the height.

How to Find the Surface Area of a Prism

To find the surface area of a prism, you will need to measure the length, width, and height of the prism. Once you have these measurements, you will multiply the length by the width to get the base area. To find the lateral area, you will need to multiply the height by the perimeter of the base. The total surface area of the prism will be the sum of the base area and lateral area.

Examples

There are an infinite number of possible prisms, but we’ll focus on three common examples – rectangular prisms, triangular prisms, and cylinders.

A rectangular prism is a 3-dimensional object with six faces that are rectangles. To find the surface area of a rectangular prism, you need to add the areas of all six faces. This is because the surface area is defined as the measure of how much exposed area the object has. So, if you took the rectangular prism and turned it upside down, all of the faces that are touching the ground would be considered exposed.

To find the surface area of a triangular prism, you start by finding the area of each triangle (base times height divided by two) and then adding those together. The triangular prism has five faces – two triangles for the ends, and three rectangles for the sides.

A cylinder is similar to a rectangular prism except that it has cylindrical sides instead of rectangular ones. To find the surface area of a cylinder, you need to find the areas of both circular ends (pi times radius squared) and add them together. Then, you need to find the area of one side (circumference times height) and multiply that by 2 (since there are two sides).

Conclusion

To find the surface area of a prism, you need to know the length of each side and the height of the prism. To find the length of each side, you need to know the measurement of one side and the measurement of one angle. To find the height of the prism, you need to know either two measurements from different sides or one measurement from a side and one from an angle. With these three pieces of information, you can calculate the surface area using either the formula for a rectangle or triangle.