Surface area of a rectangular prismTo derive the formula of the surface area of a rectangular prism, follow closely the steps below: In order to make a rectangular prism like the one shown above, you basically use the following rectangular prism template: Looking at the rectangular prism template, it is easy to see that the solid has six sides and each side is a rectangle The bottom side and the top side are equal and have l and w as dimensions The area for the top and bottom side is l× w + l × w = 2 × l × w The front side (shown in sky blue) and the back side (not shown) are equal and have h and l as dimensions The area for the front and the back side is l× h + l × h = 2 × l × h Then, the last two sides have h and w as its dimensions. One side is shown in purple The area for the front and the back side is w× h + w × h = 2 × w × h The total surface area, call it SA is: SA = 2 × l × w + 2 × l × h + 2 × w × h Example #1: Find the surface area of a rectangular prism with a length of 6 cm, a width of 4 cm, and a height of 2 cm SA = 2 × l × w + 2 × l × h + 2 × w × h SA = 2 × 6 × 4 + 2 × 6 × 2 + 2 × 4 × 2 SA = 48 + 24 + 16 SA = 88 cm^{2} Example #2: Find the surface area of a rectangular prism with a length of 4 cm, a width of 5 cm, and a height of 10 cm SA = 2 × l × w + 2 × l × h + 2 × w × h SA = 2 × 4 × 5 + 2 × 4 × 10 + 2 × 5 × 10 SA = 40 + 80 + 100 SA = 220 cm^{2} Example #3: Find the surface area with a length of 1/2 cm, a width of 8 cm, and a height of 1/4 cm SA = 2 × l × w + 2 × l × h + 2 × w × h SA = 2 × 1/2 × 8 + 2 × 1/2 × 1/4 + 2 × 8 × 1/4 SA = 1 × 8 + 1 × 1/4 + 16 × 1/4 SA = 8 + 1/4 + 4 SA = 12 + 1/4 SA = 48/4 + 1/4 SA = 49/4 cm^{2} SA = 12.25 cm^{2} 




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