Find the surface area of a rectangular prism 4 cm by 5 cm by 6 cm?
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Surface area is the total area of all faces of a three-dimensional object. In this lesson, we will find the surface area of a rectangular prism with dimensions 4 centimeters by 5 centimeters by 6 centimeters. This means we need to calculate the combined area of all six faces of the prism.
A rectangular prism has exactly 6 faces. These faces come in 3 pairs of identical rectangles. In our prism with dimensions 4 by 5 by 6 centimeters, we have two faces that are 4 by 5, two faces that are 4 by 6, and two faces that are 5 by 6. Each pair is colored differently to show their matching dimensions.
The general formula for calculating the surface area of a rectangular prism is: Surface Area equals 2 times the sum of length times width, length times height, and width times height. This formula accounts for the three pairs of faces by calculating the area of each unique face and multiplying by 2 since there are two of each.
Now we assign our specific measurements to the variables in the formula. We'll use length (l) equals 6 centimeters, width (w) equals 5 centimeters, and height (h) equals 4 centimeters. Note that the assignment of which dimension is length, width, or height can vary, but the final result will be the same.
Now we calculate each component of the formula separately. First, length times width: 6 times 5 equals 30 square centimeters. Second, length times height: 6 times 4 equals 24 square centimeters. Third, width times height: 5 times 4 equals 20 square centimeters. These represent the areas of the three unique faces of our prism.
Now we substitute our calculated values into the formula. Surface area equals 2 times the sum of 30, 24, and 20. This simplifies to 2 times 74, which equals 148 square centimeters. Therefore, the surface area of our rectangular prism is 148 square centimeters.
To verify our answer, we can calculate the area of each individual face separately and add them together. We have two 4 by 5 faces, two 4 by 6 faces, and two 5 by 6 faces. This gives us 20 plus 20 plus 24 plus 24 plus 30 plus 30, which equals 148 square centimeters. This confirms our previous calculation using the formula is correct.