Surface area of a rectangular prism
To derive the formula of the surface area of a rectangular prism, follow closely the steps below:
Start with a right rectangular prism as shown below and call the length l, the width w, and the height h:
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}

Nov 21, 19 02:38 PM
What is a probability line ? Things that you must know before doing problems ...
Read More
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.