# Right Rectangular Prism – Definition With Examples

Created on Dec 28, 2023

Updated on January 12, 2024

Geometry, one of the many branches of mathematics, can sometimes be challenging for young learners. At Brighterly, we are committed to turning complex ideas into simple, fun, and engaging learning experiences. Today, let’s delve into one of the most common three-dimensional geometric figures – the Right Rectangular Prism.

A right rectangular prism is a three-dimensional solid object where all angles are right angles, and all faces are rectangles. These shapes are found abundantly in our surroundings. They make up the basic structure of many everyday objects like books, crates, and even buildings! By understanding the properties of a right rectangular prism and knowing how to calculate its various attributes such as surface area, volume, and diagonal, children can enhance their spatial understanding and mathematical skills.

## What Is a Right Rectangular Prism?

A right rectangular prism, a commonly occurring shape in our daily lives and an integral part of our learning in geometry, refers to a solid, three-dimensional figure. The name indicates its properties – it’s a prism because it has the same cross-section along its length, it’s rectangular because the cross-section is a rectangle, and it’s right because the angles between the bases and the sides are right angles (90 degrees).

Objects such as shoe boxes, books, and bricks are practical examples of right rectangular prisms. If you think about a typical shoebox, it has six faces that meet at right angles. Each pair of opposite faces are identical rectangles, making it an excellent real-world illustration of a right rectangular prism. By studying such objects, we can enhance our understanding of three-dimensional shapes and their properties.

## Properties of a Right Rectangular Prism:

A right rectangular prism possesses certain identifiable properties that make it unique among other geometric shapes. It has six faces, and all of them are rectangles. Out of these, the opposite faces are congruent, meaning they have the same size and shape. It also has 12 edges, with all the corners meeting at a right angle.

Furthermore, if you draw a line segment connecting any two opposite corners inside the prism (known as a space diagonal), it will also intersect at a right angle with the prism’s base, hence the name, right rectangular prism. These properties allow us to solve various problems and apply our knowledge to practical applications, from architecture to computer graphics.

## Formulas of a Right Rectangular Prism

To understand the formulas related to a right rectangular prism, let’s denote the length of the prism as ‘l’, width as ‘w’, and height as ‘h’. The surface area, volume, and diagonal can then be calculated using these dimensions. These formulas allow us to calculate the amount of material needed to construct a prism (surface area), the space it occupies (volume), and the longest distance within the prism (space diagonal).

## Surface Area of a Right Rectangular Prism

The surface area of a right rectangular prism can be calculated by adding the areas of all the faces. Since it has six rectangular faces, the surface area ‘A’ is given by the formula A = 2lw + 2lh + 2wh. This formula indicates that the surface area comprises twice the product of the length and width, twice the product of length and height, and twice the product of width and height.

## Volume of Right Rectangular Prism

The volume of a right rectangular prism represents the amount of space it occupies. It can be calculated by multiplying the length, width, and height of the prism together. So, the volume ‘V’ is given by the formula V = lwh.

## Diagonal of a Right Rectangular Prism

The diagonal of a right rectangular prism, also referred to as the space diagonal, is the longest line that can be drawn within the prism. It connects two opposite corners of the prism passing through its interior. The formula for the space diagonal ‘d’ is derived from the Pythagorean theorem and given by d = √(l² + w² + h²).

## Conclusion

As we conclude our journey of exploration into the fascinating world of the right rectangular prism, we want to remind you that at Brighterly, we believe in making math fun, interactive, and easily understandable for every child. The understanding of a right rectangular prism and its properties is not just crucial for math class but also plays a vital role in many real-world applications. From constructing a building to packing a box, the concepts learned today will accompany you in many walks of life. Keep practicing, stay curious, and continue exploring the captivating world of mathematics with Brighterly!

## Frequently Asked Questions on Right Rectangular Prism

### What is a right rectangular prism?

A right rectangular prism is a three-dimensional geometric shape in which all the six faces are rectangles and all the angles are right angles. This object is termed ‘right’ due to its right angles, ‘rectangular’ for its rectangular faces, and ‘prism’ as it has the same cross-sectional shape throughout its length.

### What are the properties of a right rectangular prism?

A right rectangular prism has several unique properties. It has six faces, all of which are rectangles. The opposite faces are congruent to each other. There are 12 edges in total, and all the corners meet at a right angle. Moreover, a line segment drawn from one corner to the opposite corner inside the prism forms a right angle with the base.

### How do you calculate the surface area of a right rectangular prism?

The surface area of a right rectangular prism is calculated by adding the areas of all six faces. If the length, width, and height of the prism are ‘l’, ‘w’, and ‘h’ respectively, then the surface area ‘A’ is given by the formula A = 2lw + 2lh + 2wh.

### How do you find the volume of a right rectangular prism?

The volume of a right rectangular prism is the amount of space it occupies. It can be calculated by multiplying the length, width, and height of the prism. So, if ‘l’, ‘w’, and ‘h’ are the length, width, and height, respectively, the volume ‘V’ is given by the formula V = lwh.

### What is the formula for the diagonal of a right rectangular prism?

The diagonal of a right rectangular prism, also known as the space diagonal, is the longest line that can be drawn within the prism. It connects two opposite corners of the prism passing through its interior. Using the Pythagorean theorem, if ‘l’, ‘w’, and ‘h’ are the length, width, and height, respectively, the space diagonal ‘d’ is given by the formula d = √(l² + w² + h²).

## Information Sources:

- “Computer Graphics” – Wikipedia
- “Geometric Solids” – National Council of Teachers of Mathematics
- “Volume Formulas” – Wolfram MathWorld