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**Rectangular Prism|Definition & Meaning**

**Definition**

A **rectangular** **prism** or **cuboid** is a **type** of **regular** **prism** (three-dimensional closed solid) **where** the **two base faces** are **rectangles.** By the definition of a prism, all six **faces** of a **rectangular prism look** like **rectangles.**

**Real World Applications **

**Rectangular prisms** are **used** in many **real-world applications.** Here are a few examples.

Figure 1 – Illustration of rectangular prism used in various applications in daily life

**Boxes:**Many**commonplace things**come**packaged**in**rectangular prisms,**including**cereal boxes, shoe boxes,**and**gift boxes.****Buildings:**A rectangular prism can roughly**represent**the**shape**of many different types of**structures,**including**homes**and**office buildings.**- Rectangular prisms are
**frequently used**as**storage**and**transportation**containers.**Bins, barrels,**and**shipping containers**are a few examples. **Furniture:**The rectangular prism shape is the**basis**for many items of**furniture,**including**tables, workstations,**and**bookshelves.****Packaging:**Many**goods come**in**rectangular prism-shaped containers,**such as**milk cartons,**and**soda cans.****Geometry:**Rectangular prisms are used to**teach ideas**like**volume**and**surface area**in geometry.

**The Volume of Rectangular Prism**

Figure 2 – Volume of Rectangular Prism

The **amount** of **space** a **rectangular prism takes** up is **measured by** its **volume.** It **serves** as a **gauge for** the **capacity** of the rectangular prism. It is **calculated** by **multiplying** the **rectangular** prism’s **length, width,** and **height.**

**Volume** = L x W x H

Here, **V, L, W**, and **H** are (respectively) the **volume**, **length, width,** and **height** of the rectangular prism.

**Surface Area of Rectangular Prism**

For a rectangular prism, the **surface area** is the **total area** of all of its faces. It is the **sum** of the **areas** of the **six rectangular faces** of the prism.

**Surface Area** = 2LW + 2LH + 2WH

Here, **SA, L, W, and H** are (respectively) the **surface area, length, width,** and **height** of the rectangular prism.

**Properties of Rectangular Prism**

Following are some important properties of a rectangular prism:

- It has
**six rectangular faces,**all of which are present. - The
**intersection points**of the edges, or vertices, are**eight.** - It has a total of
**12 straight edges.** - It features
**three parallel pairs**of**faces**on each side. - It features
**three opposed**yet**congruent sets**of**faces**(the same size and shape). - A rectangular prism’s
**opposing faces**are**parallel**to**one another**as well. - A rectangular prism has a
**length, breadth,**and**height**that are all**perpendicular**to**one another.** - A rectangular prism’s
**volume**is**determined**by**multiplying**its**length**by its**width**by its**height.** - A rectangular prism’s
**surface area**is equal to the**sum**of**all**of its**faces****surface areas.** - A rectangular
**prism contains depth**in**addition**to**length**and**width**because it is a three-dimensional shape.

**Right Rectangular Prism vs. Oblique Rectangular Prism**

A **right rectangular prism** is a particular kind of rectangular prism that has **right angles** at each of its **vertices** and **faces** that are **all perpendicular** to one another. On the other hand, the **faces** of an **oblique** rectangular **prism** are **not parallel** to one another.

Here are some other **distinctions** between **right** and **oblique rectangular prisms.**

**Shape:**A**right**rectangular**prism**has**straight edges,**and right angles at all four corners, and is a regular shape. An irregular shape, an**oblique**rectangular**prism**has**edges**that aren’t**always straight**and corners that aren’t always at right angles.**Dimensions:**A**right**rectangular**prism**has**length, breadth,**and**height**that are all**perpendicular**to one another. An**oblique**rectangular**prism’s**dimensions are**not always parallel**to one another.**Volume:**The formula**V = Length x Width x Height**can be used to**determine**the**volume**of a**right**rectangular**prism.**L stands for length, w for width, and h for height. This**formula cannot**be**used**to**determine**the**volume**of an oblique rectangular prism because the**dimensions**are**not parallel.****Surface area:**The f**ormula SA = 2lw + 2lh + 2wh**can be used to get the surface area of a right rectangular prism. L stands for length, w for width, and h for height. This**formula cannot**be used to**get**the**surface area**of an**oblique rectangular prism**because the**dimensions**are**not parallel.**

**Rectangular Prism as a Lunch Box**

Figure 3 – Rectangular Prism as a Lunch Box

One **example** of a **daily life scenario** where a **rectangular prism** might be **used** is **packing** a **lunch.** Here’s how a rectangular prism could be used in this scenario.

**Pick a lunchbox:**A**lunch box**is often a**rectangular prism**with adjustable length, breadth, and height to hold various food items.**Make a lunch:**To make the most of the available space in the lunch box, the**foods**being**packed,**such as**sandwiches, fruits,**and snacks,**can**be**arranged.**The**amount**of**food**that**can fit**within the**lunch box**may be calculated using its length, width, and height.**Close the Lunch Box:**After the food has been packed, the**lunch box**can be**closed**and**kept shut**with a latch or zipper. The lunch box’s**rectangular prism**form**helps**to**retain**the**food**and**protect**it from**leaking out.****Transport the Lunch Box:**The**lunch box’s**handle or shoulder strap can be**used**to**transport**it to**school**or**work.**The**lunch box**is**convenient**to**keep**and**travel thanks to**its**rectangular prism design.**- When it’s
**time to eat,**open the lunchbox so that the contents can be taken out and devoured. The**lunch box’s rectangular prism design makes**it**simple**to**reach**the**contents within.**

**Solved Examples With Rectangular Prisms**

**Example 1**

Figure 4 – Finding the volume of rectangular prism an example

**Consider** a **rectangular prism** having a **length** of **4 cm,** a **height** of **8 cm,** and a **width** of **16 cm. Calculate** the **volume** of this rectangular prism.

**Solution**

Length = 4 cm

Height = 8 cm

Width = 16 cm

Volume = ?

As we know:

Volume = Length x Width x Height

Volume = 4 cm x 16 cm x 8 cm

Volume = 512 cm$^{3}$

**Example 2**

**Consider** a **rectangular** prism having a length of **4cm,** a **height** of **8cm,** and a **width** of **16cm calculate** the **surface area** of this rectangular prism.

**Solution**

Length = 4 cm

Height = 8 cm

Width = 16 cm

Volume = ?

As we know:

Surface Area = 2LW + 2LH + 2WH

Surface Area = 2(4 cm)(16 cm) + 2(4 cm)(8 cm) + 2(16 cm)(8 cm)

Surface Area = 448 sq.cm

*All mathematical drawings and images were created with GeoGebra.*