# Surface Area of a Rectangular Prism

A rectangular prism, like other three-dimensional shapes, has a surface area and volume. The net area of the prism is its surface area. Let us go over the definition, types, surface area, and volume of a rectangular prism in detail in this article.

## What is a Rectangular Prism?

A rectangular prism is a three-dimensional shape with six faces in geometry.

(two at the top and bottom and four are lateral faces). The prism’s faces are all rectangular.

As a result, there are three sets of identical faces here.

We also know a rectangular prism as a cuboid due to its shape.

We can find a rectangular prism in everyday objects such as a geometry box, notebooks, diaries, and rooms.

Geometry is the study of shapes and object configuration.

### Rectangular Prism Properties

A rectangular prism has six faces, twelve edges, and eight vertices.

The rectangular prism’s top and bottom are always rectangles.

It, like the cuboid, has three dimensions: length, width, and height.

Identical or congruent pairs of opposite faces

The lateral faces of a right rectangular prism are rectangles.

The lateral faces of an oblique rectangular prism are parallelograms.

It has a square cross-section.

It appears to be a cuboid.

#### Rectangular Prism Varieties

Rectangular prisms are divided into two types. They are:

#### Right Rectangular Prism

A rectangular prism is one with rectangular bases.

A right rectangular prism is a prism with six rectangle faces and all angles being right angles.

Vertices of a rectangular prism = 8

Edges of a rectangular prism = 12

Faces of a rectangular prism = 6 (including bases)

#### Oblique Rectangular Prism

An oblique prism is one in which the bases are not perpendicular to each other.

This rectangular prism is one with bases that are not directly above each other.

### Formulas for Rectangular Prisms

A three-dimensional object is a rectangular prism. As a result, it will have a surface area and a volume.

The length of a prism’s sides or edges is required to calculate its volume and surface area.

Let ‘l’, ‘w’, and ‘h’ represent the rectangular prism’s length, width, and height.

We can find the formulas below.

#### Rectangular Prism Volume Formula

The volume of a rectangular prism is a measurement of the prism’s occupied units.

Cubic units are used to represent the volume of a rectangular prism.

It is also the number of units required to fill a rectangular prism.

The volume of a rectangular prism is equal to the area of the base multiplied by its height.

As a result, the volume of a rectangular prism formula is as follows:

A rectangular prism’s volume equals the sum of its length, width, and height in cubic units.

Cubic units of volume = l x w x h

#### Rectangular Prism Surface Area

A rectangular prism’s surface area is a measure of how much-exposed area it has.

We measure the surface area in square units.

The total surface area of a rectangular prism is the sum of its lateral surface area (LSA) and twice its base area.

LSA + 2 (Base area) [Square units] = Total Surface Area of Rectangular Prism

A rectangular prism’s lateral surface area is the sum of the surface areas of all its faces, excluding the base.

The lateral surface area of any right rectangular prism is equal to the perimeter of the base multiplied by the prism’s height.

As a result, the lateral surface area is equal to P x h [Square units].

Where:

P. denote the perimeter of a base.

h is the prism’s height.

The rectangular prism perimeter is

P = 2 (l + w)

As a result, a rectangular prism’s lateral surface area (LSA) equals 2 (l + w) h square units.

Hence,

TSA = LSA + 2 (Base Area) = 2 (l + w) h + 2 (l x w) = 2 lh + 2 wh + 2 lw [Square units]

As a result, the surface area of a rectangular prism formula is as follows:

A rectangular prism’s surface area equals 2 (lh + wh + lw) square units.

### Surface Area of a Rectangular Prism Examples

1. Marilyn will need to purchase cardboard to construct a 7-foot-long, 5-foot-wide, and 9-foot-high box without a lid. What quantity of cardboard should she purchase?

Solution:

The box’s dimensions are as follows:

l = 7 feet in length

b = 5 feet in breadth

h = 9 feet tall

To determine the amount of cardboard needed, we must first determine the total area of the open box.

The total area of five surfaces can be used to calculate the area of an open box (a box without a lid).

lb. base area

Area of the four lateral faces or lateral surface area:

2(l + b)h = 2lh + 2bh

Total surface area of the rectangular prism (open box) = 7 * 5 + 2 * 7 * 9 + 2 *5 * 9

= 35 + 126 + 90 = 251 inch2

Marilyn should purchase 251 inch2 of cardboard.

2. A rectangular prism has a total surface area of 76 ft2, a base area of 10 ft2, and a perimeter of 14 ft. Determine the height of a prism using the surface area formula.

Solution:

Let l, b, and h represent the rectangular prism’s length, breadth, and height, respectively.

lb = 10 ft2 base area

2(l + b) = 14 ft is the perimeter of the base.

76 ft2  = surface area

Using the surface area of a rectangular prism formula

Total surface area = 2(lb + bh + lh) = 76 ft2

Alternatively, 2lb + 2(l+b)h = 76 ft 2

Changing the values, we have,

2 x 10 + 14 x h = 76

20 + 14 x h = 76

14 x h =56

h = 56/14 = 4ft

The prism stands 4 feet tall.

1. How do You get the Surface Area of a Rectangular Prism?

A = 2wl + 2lh + 2hw is the formula for calculating the surface area of a rectangular prism, where w is the width, l is the length, and h is the height.

We enter our values into this formula and then evaluate.

2. What is the Surface Area in a Math Rectangular Prism?

Finding the total area of all six faces of a rectangular prism allows you to calculate its total surface area.

The formula for calculating the surface area of a rectangular prism is as follows:

A rectangular prism’s total surface area equals 2(lb + bh + lh) square units.

3. What is the Formula for the Surface Area?

The cuboid’s surface area formula is 2(lb + bh + hl).

The letters “l,” “b,” and “h” represent the cuboid’s three dimensions: length, breadth, and height.

### More FAQs

4. What is the Formula of a Rectangle Prism?

Volume = length * width * height is the formula for calculating the volume of a rectangular prism.

If double the length and cut the height in half, the volume is V = (2l) (w) (1/2h).

5. How do You Find the Lateral Area and Surface Area of a Rectangular Prism?

The lateral surface area of any right rectangular prism is equal to the perimeter of the base multiplied by the prism’s height.

As a result, a rectangular prism’s lateral surface area (LSA) equals 2 (l + w) h square units.

6. What is the Formula for the Surface Area of a Rectangle?

A square is a type of rectangle that has all equal sides.

How do you calculate the area of a square?

Divide the length by the length. Step 2: L X L = L2, where L denotes the length of one side.