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Surface Area Of Rectangular Prism – Definition, Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Surface Area of Rectangular PrismSurface Area Of Rectangular Prism – Definition, ExamplesTable of ContentsSurface Area of Rectangular Prism Definition of Surface Area of Rectangular Prism

The surface area of a rectangular prism refers to the total area covered by all the surfaces of the prism. A rectangular prism consists of 6 faces, each being a rectangle, with the bases being congruent and parallel to each other. This three-dimensional shape, also known as a cuboid, has two types: right rectangular prisms and oblique rectangular prisms, with the right rectangular prism having faces perpendicular to its bases.

The surface area can be studied in two main parts: the base areas and the lateral surface area. The base areas include the area of two rectangles at its base. The Lateral Surface Area (LSA) involves the area of the faces excluding the base and top, similar to calculating the area needed to paint just the walls of a room. The Total Surface Area (TSA) encompasses the area of all faces including both the bases and the lateral surface area.

Examples of Surface Area of Rectangular Prism Example 1: Finding the Lateral Surface Area of a Rectangular Prism Problem:

What is the lateral surface area of a rectangular prism with length 10 m, breadth 8 m and height 2 m?

Finding the Lateral Surface Area of a Rectangular Prism

Step-by-step solution:

Step 1, Write down the given measurements: length (l) = 10 m, width (w) = 8 m, height (h) = 2 m.

Step 2, Apply the formula for lateral surface area: LSA = 2h(l + w).

Step 3, Substitute the values into the formula: LSA = 2 × 2 × (10 + 8)

Step 4, Calculate the sum inside the parentheses: LSA = 4 × 18

Step 5, Multiply to find the final answer: LSA = 72 square meters

Example 2: Calculating the Total Surface Area of a Rectangular Prism Problem:

What is the total surface area of a rectangular prism with length 42 inches, breadth 30 inches and height 15 inches?

Calculating the Total Surface Area of a Rectangular Prism

Step-by-step solution:

Step 1, Write down the given measurements: length (l) = 42 in, breadth (b) = 30 in, height (h) = 15 in.

Step 2, Use the formula for total surface area: TSA = 2(lb + bh + hl).

Step 3, Substitute the values into the formula: TSA = 2(42 × 30 + 30 × 15 + 15 × 42)

Step 4, Calculate each product inside the parentheses: TSA = 2(1,260 + 450 + 630)

Step 5, Add all products: TSA = 2 × 2,340

Step 6, Multiply to get the final answer: TSA = 4,680 square inches

Example 3: Box with an Open Top Problem:

Emily built a rectangular box with an open top. The box is 12 inches long, 5 inches wide, and 9 inches high. How much cardboard should she buy?

Box with an Open Top

Step-by-step solution:

Step 1, Note that since the box has an open top, we won't include the area of the top face.

Step 2, Write down the given dimensions: length (l) = 12 inches, width (w) = 5 inches, height (h) = 9 inches.

Step 3, The surface area will include the bottom face and all four side faces. We can write this as: Surface Area = lw + 2hl + 2hw

Step 4, This can also be written as: Surface Area = lw + 2h(l + w)

Step 5, Substitute the values: Surface Area = (12 × 5) + 2 × 9 × (12 + 5)

Step 6, Calculate the first part (bottom area): Surface Area = 60 + 2 × 9 × 17

Step 7, Calculate the second part (sides area): Surface Area = 60 + 306

Step 8, Add to get the total: Surface Area = 366 square inches

Comments(5)GGardenerNinaNovember 4, 2025I've been struggling to explain surface area to my students. This page's clear def and examples made it a breeze! Thanks!

NNatureLover25September 16, 2025I used this page to help my kids with their math homework, and it was a lifesaver! The examples are super clear, and the step-by-step explanations made it so easy to follow. Highly recommend it!

NNatureLover89September 10, 2025I used this page to help my son with his math homework, and it was a lifesaver! The examples were super clear, and he finally understood how to calculate the surface area. Thanks for making math less stressful!

NNatureLover2025August 27, 2025This page was super helpful for explaining the surface area of a rectangular prism to my son. The step-by-step examples made it so easy for him to follow. We even used it to solve his homework together!

NNatureLover92August 6, 2025This page was super helpful for my son's math homework! The examples are clear, and he finally gets how to calculate the surface area of a rectangular prism. Thanks for breaking it down!

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