Video: Finding the Area of One Face of a Cube given Its Total Surface Area

Given that a cube has a surface area of 234 ft², determine the area of one of its faces.

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Video Transcript

Given that a cube has a surface area of 234 feet squared, determine the area of one of its faces.

The surface area of a cube is the area of all six faces added together. Here is a net of a cube. When we draw a net, we can see all six faces of a cube. The space of all six of these faces add up to 234 feet squared. What would one of the sides be?

Remember that 234 is all six sides together and we need one side. To find one side, we’ll divide the total surface area by six. If we take 234, divide it by six, we’ll know the surface area of each individual face. To divide, we ask, how many times does six go into 23? It goes three times. Three times six equals 18. 23 minus 18 equals five. Bring down the four. How many times can six be divided into 54? Nine times. Nine times six equals 54. 54 minus 54 equals zero.

So we know that 234 is evenly divisible by six and each individual face measures 39 feet. When you’re given the total surface area of a cube, you can divide that value by six to find the area of its faces. In this case, each face has an area of 39 feet squared.

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