In a cuboid, the length, width and height may be of different lengths. A cube is a special case of a cuboid in which all six faces are squares.
To calculate the surface area of the cuboid we need to first calculate the area of each face and the add up all the areas to get the total surface area.
Total area of top and bottom surfaces is lw + lw = 2lw
Total area of front and back surfaces is lh + lh = 2lh
Total area of the two side surfaces is wh + wh = 2wh
Surface area of cuboid = 2lw + 2lh + 2wh = 2(lw + lh + wh)
Volume of rectangular prism = lwh
Find the surface area of the following cuboid.
Total area of top and bottom surfaces is 2 × 5 × 6 = 60 in2
Total area of front and back surfaces is 2 × 5 × 3 = 30 in2
Total area of the two side surfaces is 2 × 6 × 3 = 36 in2
Surface area of cuboid = 60 + 30 + 36 = 126 in2
l = 6 in, w = 5 in and h = 3 in
Surface area of cuboid = 2(lw + lh + wh) = 2 (6 × 5 + 6 × 3 + 5 × 3) = 126 in2
Another way to look at the surface area of a cuboid is to consider a net of the cuboid. The net is a 2-dimensional figure that can be folded to form a 3-dimensional object.
Imagine making cuts along some edges of a cuboid and opening it up to form a plane figure. The plane figure is called the net of the cuboid.
The following net can be folded along the dotted lines to form the cuboid.
We can then calculate the area of each rectangle in the net and add them up to get the surface area of the cuboid. These videos show how to find the surface area of a rectangular prism using nets.
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