Find the surface area of a rectangular prism 4 cm by 4 cm by 5 cm?
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Surface area is the total area of all faces of a three-dimensional object. In this lesson, we'll find the surface area of a rectangular prism with dimensions 4 centimeters by 4 centimeters by 5 centimeters. Our goal is to calculate the sum of the areas of all six faces.
A rectangular prism has exactly six faces. These faces are arranged in three pairs of opposite faces. To better visualize all faces, we can unfold the prism into a net diagram. This shows all six faces clearly. The three different face types are: front and back faces, left and right faces, and top and bottom faces. Notice that opposite faces are identical in shape and size.
Now let's calculate the area of each face type systematically. For the front and back faces, we multiply length by height: 4 times 5 equals 20 square centimeters. For the left and right faces, we also multiply width by height: 4 times 5 equals 20 square centimeters. For the top and bottom faces, we multiply length by width: 4 times 4 equals 16 square centimeters.
We can use a systematic formula to find the surface area of any rectangular prism. The formula is: Surface Area equals 2 times the quantity length times width, plus length times height, plus width times height. Substituting our dimensions where length equals 4, width equals 4, and height equals 5, we calculate each term. Length times width is 4 times 4 equals 16. Length times height is 4 times 5 equals 20. Width times height is 4 times 5 equals 20. Adding these together gives 16 plus 20 plus 20 equals 56. Finally, multiplying by 2 gives us a surface area of 112 square centimeters.
Let's verify our answer by adding the individual face areas. We have two faces with area 20 square centimeters, two faces with area 20 square centimeters, and two faces with area 16 square centimeters. This gives us 2 times 20 plus 2 times 20 plus 2 times 16, which equals 40 plus 40 plus 32, totaling 112 square centimeters. Both methods give the same result, confirming our answer. The final answer is: Surface Area equals 112 square centimeters. The key steps for solving similar problems are: first, identify the face types; second, calculate each face area; and third, sum all the areas.