Surface Area of Rectangular Prism Examples

Example 1: Determine the total surface area of a rectangular prism if its lateral surface area is 560 sq. cm and the length and breadth of the base are 12 cm and 8 cm, respectively.

Solution:

Given,

• Length of the rectangular base (l) = 12 cm
• Breadth of the rectangular base (b) = 8 cm
• Lateral surface area of the prism (LSA) = 560 sq. cm

We have,

Total surface area of a prism (TSA) = LSA + 2 × Base area

Base Area = 2(l + b)

= 2 × (12 + 8) = 2 × 20 = 40 sq. cm

TSA = 560 + 2 × 40

= 560 + 80 = 640 sq. cm

Hence, the rectangular prism’s total surface area is 640 sq. cm.

Example 2: Calculate the length of the base of a rectangular prism if its height is 9 inches and the breadth of the base is 4 inches, and the lateral surface area is 198 sq. in.

Solution:

Given,

• Lateral surface area = 198 sq. in
• Breadth of Rectangular base (b) = 4 inches
• Height = 9 inches

Length of Rectangular base (l) = ?

We have,

Lateral Surface Area of a Rectangular Prism = 2h (l + b) square units

⇒ 2 × 9 × (l + 4) = 198

⇒ 18 × (l + 4) = 198

⇒ l + 4 = 198/18 = 11

⇒ l = 11 − 4 = 7 in

Thus, length of the rectangular prism is 7 inches.

Example 3: Find the lateral surface area of a rectangular prism if its height is 18 cm and the length and breadth of the base are 14 cm and 10 cm, respectively.

Solution:

Given,

• Length of Rectangular base (l) = 14 cm
• Breadth of Rectangular base (b) = 10 cm
• Height = 18 cm

We know that,

Lateral Surface Area of a Rectangular Prism = 2h (l + b) square units

= 2 × 18 × (14 + 10)

= 36 × 24 = 864 sq. cm

Hence, the lateral surface of the given prism is 864 sq. cm.

Example 4: Determine the surface area of a rectangular prism if its height is 12 cm and the length and breadth of the base are 8 cm and 5 cm, respectively.

Solution:

Given,

• Length of Rectangular base (l) = 8 cm
• Breadth of Rectangular base (b) = 5 cm
• Height = 12 cm

We have,

Total Surface Area of a Rectangular Prism = 2(lb + bh + lh) square units

= 2 × (8 × 5 + 5 × 12 + 8 × 12)

= 2 × (40 + 60 + 96)

= 2 × 196 = 392 square units

Hence, the rectangular prism’s surface area is 392 square units.

Example 5: Determine the surface area of a rectangular prism if its height is 14 units and the length and breadth of the base are 10 units and 7 units, respectively.

Solution:

Given,

• Length of Rectangular base (l) = 10 units
• Breadth of Rectangular base (b) = 7 units
• Height = 14 units

We have,

Total Surface Area of a Rectangular Prism = 2(lb + bh + lh) square units

= 2 × (10 × 7 + 7 × 14 + 10 × 14)

= 2 × (70 + 98 + 140)

= 2 × 308 = 616 square units

Hence, the rectangular prism’s total surface area is 616 square units.

Surface Area of a Rectangular Prism is the area covered by all the surfaces of the rectangular prism. A rectangular prism is a 3-D geometrical figure with four lateral faces with two congruent and parallel faces. A rectangular prism has a total of six faces where the opposite faces are identical, i.e., a rectangular prism has three pairs of identical faces. The dimensions of a rectangular prism are length, width, and height. It has a total of six faces, twelve edges, and eight vertices.

In this article, we will learn about the Surface Area of a Rectangular Prism (Right Rectangular Prism), the Lateral Surface Area of a (Right) Rectangular Prism, the Total Surface Area of a (Right) Rectangular Prism, and others in detail.