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### Course: 7th grade foundations (Eureka Math/EngageNY)>Unit 6

Lesson 3: Topic D: Foundations

# Surface area of a box (cuboid)

Surface area is total area on the surface of a three-dimensional shape. To find the surface area of a cuboid which has 6 rectangular faces, add the areas of all 6 faces. Or, you can label the length (l), width (w), and height (h) of the cuboid and use the formula: surface area (SA)=2lw+2lh+2hw.

## Want to join the conversation?

• what is a cuboid and why use a cereal box.
• Palomo’s reply was confusing. A cuboid is basically a box. A cereal box is a good example of a cuboid.
• what if all i get for length is fractions?
• That's totally ok! You just have to find the numbers you can multiply most easily in a specific order.
• does SIDE and FACE means the same things? that is surface area?
• the SIDE and the FACE are the same things in usual context.
One SIDE of a square is going to be equal to all the other SIDES of a square. A side is a face.
• why do they make it so hard 😢
• It means that you are learning something which takes time to tackle. It doesn't happen in a day or even in a few.
• how do you get the surface area?
• The surface area of the rectangular prism(or cube)
is S=Ph+2B
S=Surface Area
P=perimeter of the base(you can choose any two parallel sides for the base)
h=height between 2 bases
2B=area of bases times 2
• So, if I was to calculate the area of cuboid and the volume, would it be close in value? 600 is the volume of that box and 580 is the area, but are these two values always proportional?
• No, they have no relation. The area of the cuboid isn't proportional to the volume. If the proportions of the sides are given, yes, but as a general rule, they aren't.
• Is there a more simpler formula to find the surface area of a cubiod? I don't understand the meaning of SA=2lw+2lh+2hw, my teacher told me a different formula to figure out the surface area of a cuboid but I forgot it.
• Not unless it is a perfect cube (I.e. all sides have same length l=h=w). If, and only if, that is the case, then that formula you have simplifies to SA = 6x^2.
• Were did the 60 come from? What do you do first when you got only 2 numbers?
• OK, lets go through this piece by piece. There are 6 sides to the box with the following dimensions:
Front is 20 cm by 10 cm
Back is 20 cm by 10 cm
Left is 20 cm by 3 cm
Right is 20 cm by 3 cm
Top is 10 cm by 3 cm
Bottom is 10 cm by 3 cm

Their areas are:
Front: 20 * 10 = 200 cm^2
Back: 20 * 10 = 200 cm^2
Left: 20 * 3 = 60 cm^2
Right: 20 * 3 = 60 cm^2
Top: 10 * 3 = 30 cm^2
Bottom: 10 * 3 = 30 cm^2

So the area is 200 + 200 + 60 + 60 + 30 + 30 = 580