Last updated on July 31st, 2025
A box, also known as a rectangular prism, is a 3-dimensional shape with six rectangular faces. The surface area of a box is the total area covered by its outer surface. In this article, we will learn about the surface area of a box.
The surface area of a box is the total area occupied by the boundary or surface of a box. It is measured in square units.
A box is a 3D shape with six faces, twelve edges, and eight vertices. Each face of a box is a rectangle, and opposite faces are equal. The surface area of a box includes the area of all six rectangular faces.
A box has six rectangular faces, and the surface area is the sum of the areas of all these faces.
The formula for the surface area of a box with length (l), width (w), and height (h) is given as: Surface Area = 2(lw + lh + wh) square units
To calculate the surface area of a box, add up the areas of all six faces. The formula involves multiplying each pair of dimensions (length, width, and height) and then summing these products. Multiply the result by 2 to account for opposite faces being equal.
Surface Area = 2(lw + lh + wh)
Consider a box with length 4 cm, width 3 cm, and height 5 cm.
Using the surface area formula: Surface Area = 2(lw + lh + wh) = 2(4×3 + 4×5 + 3×5) = 2(12 + 20 + 15) = 2×47 = 94 cm²
The volume of a box tells us how much space is inside it. The volume can be found by multiplying its length, width, and height.
The formula is: Volume = l × w × h cubic units
A common error is forgetting to multiply the sum of the face areas by 2, which accounts for both sets of opposite faces.
Ensure you use the complete formula: Surface Area = 2(lw + lh + wh).
Using the formula: Surface Area = 2(lw + lh + wh) = 2(5×4 + 5×3 + 4×3) = 2(20 + 15 + 12) = 2×47 = 94 cm²
Find the surface area of a box with dimensions 8 m by 6 m by 2 m.
Surface Area = 112 m²
Using the formula: Surface Area = 2(lw + lh + wh) = 2(8×6 + 8×2 + 6×2) = 2(48 + 16 + 12) = 2×76 = 152 m²
A box has a length of 10 in, a width of 7 in, and a height of 4 in. Find the surface area.
Surface Area = 268 in²
Using the formula: Surface Area = 2(lw + lh + wh) = 2(10×7 + 10×4 + 7×4) = 2(70 + 40 + 28) = 2×138 = 276 in²
Find the surface area of a box with dimensions 9 ft by 5 ft by 3 ft.
Surface Area = 174 ft²
Using the formula: Surface Area = 2(lw + lh + wh) = 2(9×5 + 9×3 + 5×3) = 2(45 + 27 + 15) = 2×87 = 174 ft²
A box with dimensions 12 cm by 10 cm by 8 cm has a surface area of what?
Surface Area = 592 cm²
Students often make mistakes while calculating the surface area of a box, which leads to wrong answers. Below are some common mistakes and the ways to avoid them.
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