Last updated on July 30th, 2025
A rectangular solid, also known as a rectangular prism, is a 3-dimensional shape with six faces, all of which are rectangles. The surface area of a rectangular solid is the total area covered by its outer surface. In this article, we will learn about the surface area of a rectangular solid.
The surface area of a rectangular solid is the total area occupied by the boundary or surface of the shape. It is measured in square units.
A rectangular solid is a 3D shape that has length, width, and height. Each of its faces is a rectangle, and it has six faces in total.
To find the surface area, you calculate the area of each face and then sum them up. A rectangular solid can also be referred to as a box.
A rectangular solid has six rectangular faces, and its surface area includes the area of each of these faces. Look at the rectangular solid below to see its surface area, length (l), width (w), and height (h).
A rectangular solid has six faces with the following formula for the surface area:
Surface Area = 2(lw + lh + wh) square units
To calculate the surface area of a rectangular solid, we need to find the area of each of its six rectangular faces and sum them up. The formula for the surface area is:
Surface Area = 2(lw + lh + wh)
Here, l is the length, w is the width, and h is the height of the rectangular solid.
Consider a rectangular solid with a length of 5 cm, a width of 3 cm, and a height of 4 cm.
To find the total surface area, we use the formula:
Surface Area = 2(lw + lh + wh) = 2(5 × 3 + 5 × 4 + 3 × 4) = 2(15 + 20 + 12) = 2 × 47 = 94 cm²
The volume of a rectangular solid shows how much space is inside it. It tells us the capacity of the solid or how much it can hold.
The volume can be found by using the formula: Volume = l × w × h (cubic units)
Students sometimes confuse the formulas for surface area and volume. Remember that surface area involves adding the areas of all the faces, while volume is the product of length, width, and height.
Given l = 7 cm, w = 4 cm, h = 3 cm. Use the formula: Surface Area = 2(lw + lh + wh) = 2(7 × 4 + 7 × 3 + 4 × 3) = 2(28 + 21 + 12) = 2 × 61 = 122 cm²
Find the surface area of a rectangular solid with a length of 5 cm, width of 6 cm, and height of 2 cm.
Surface Area = 104 cm²
Use the formula: Surface Area = 2(lw + lh + wh) = 2(5 × 6 + 5 × 2 + 6 × 2) = 2(30 + 10 + 12) = 2 × 52 = 104 cm²
A rectangular solid has a length of 8 cm, width of 5 cm, and height of 4 cm. Find the surface area.
Surface Area = 184 cm²
Use the formula: Surface Area = 2(lw + lh + wh) = 2(8 × 5 + 8 × 4 + 5 × 4) = 2(40 + 32 + 20) = 2 × 92 = 184 cm²
Find the surface area of a rectangular solid with a length of 6 cm, width of 3 cm, and height of 2 cm.
Surface Area = 72 cm²
Surface Area = 2(lw + lh + wh) = 2(6 × 3 + 6 × 2 + 3 × 2) = 2(18 + 12 + 6) = 2 × 36 = 72 cm²
The surface area of a rectangular solid is 150 cm². If the length is 5 cm and the width is 3 cm, find the height.
Height = 5 cm
Students often make mistakes while calculating the surface area of a rectangular solid, which leads to wrong answers. Below are some common mistakes and the ways to avoid them.
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