A rectangular prism has a length of 12 centimeters a width of 6 centimeters and
a height of 13 centimeters. Determine the surface area. A rectangular prism is a
three-dimensional object or solid that has six faces that are rectangles. The
surface area is equal to the number of square units it takes to cover the
outside of the rectangular prism, and because there are six faces. To
determine the surface area, we need to determine the sum of the area of these
six faces. The surface area is given by the formula s equals two times the
length times the height plus two times the length times the width plus two
times the width times the height. Two times the length times the height gives
us the area of the front face and back face. Two times the length times the
width gives us the area of the bottom and top face, and two times the width
times the height gives us the area of the right face and the left face, which
is the reason why this sum gives us the area of the six faces, which is the
surface area of the rectangular prism. Going back to our problem, the length is
12 centimeters. The width is 6 centimeters, and the height is 13
centimeters, which means the surface area S is equal to again 2 times the length
times the height is 2 times 12 centimeters times 13 centimeters, plus 2
times the length times the width is 2 times 12 centimeters times 6 centimeters
plus 2 times the width times the height is 2 times 6 centimeters times 13
centimeters. Notice how I did leave the units on the length, width, and height.
This emphasizes the units of the surface area. Notice centimeters times
centimeters is square centimeters, which will be the units for the surface area.
However we often leave the units off and until the very end and write the surface
area as S equals two times 12 times 13 plus 2 times 12 times 6 plus 2 times 6
times 13. The next step is to determine the products from left to right. 2 times
12 is 24 and now we need to find 24 times 13. First multiplied by 3. 3 times 4
is 12. Record the 2, perform an exchange with
the 1. Next we have 3 times 2 plus 1 which is 7. Before multiplying by the one we
recorded a 0 in the ones place value. And now we have 1 times 4 which is 4 and 1
times 2 which is 2 and now we add. 2 plus 0 is 2. 7 plus 4 is 11. Record the one
Perform an exchange. 1 plus 2 is 3. The first product is 312. Now we have plus 2
times 12 is 24. 24 times 6 is 144, which if we need to we can check. 6 times 4 is
24. Record the 4 and perform an exchange with
the 2. 6 times 2 is 12 plus 2 is 14, giving us 144. And then we have plus 2
times 6 is 12. 12 times 13 is 156, which if we need to make in check. Multiplying
by 3, 3 times 2 is 6. 3 times 1 is 3. Record a 0 below the 6. 1 times 2 is 2. 1
times 1 is 1, which does give us 156. The last step is to determine the sum. The
surface area S equals 312 plus 144 plus 156 which equals 612, and again the units
are square centimeters. Of course, if we need to we can check the sum,
giving us a sum of 612. We know the surface area is now 612 square
centimeters, which means it would take 612 square centimeters to cover the
outside of the rectangular prism. Let's also write the result as a complete
sentence. The rectangular prism has a surface area of 612 square centimeters.
I hope you found this helpful.