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} 




Are you a fan of this site? Support us Our awards! Our partners About me Disclaimer Build your website! Advertise on my site Try our free toolbar Like us on Facebook Take our survey 

