How to Find the Surface Area of a Box
Add together the area of each side to get the surface area of the box., Measure the length of the box., Measure the height of the box, or the distance from the floor to the top., Measure the width of the box., Ensure that you didn't measure the same...
Step-by-Step Guide
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Step 1: Add together the area of each side to get the surface area of the box.
Surface area is the total area of each side.
As long as you know how to find the area of a regular rectangle, which is simply the length times the height, you can find each side and add them together.
However, there is also a simplified formula that will do this for you if you know the measurements of the box:
SurfaceArea=2lw+2lh+2wh{\displaystyle SurfaceArea=2lw+2lh+2wh} l is the length of the box, or the longest side. h is the height of the box. w is the width of the box. -
Step 2: Measure the length of the box.
This is your longest side.
There should be 4 identical lines equally long across the whole box.
Lay the box down on it's longest side to make it easier to measure.
Example:
The length of the box is 5 feet. , Make sure you don't measure the same side as the length.
Example:
The height of the box is 4 feet. , This is the side directly perpendicular (it forms a right angle, or L) with the length.
Make sure you are not remeasuring the height.
Example:
The width of the box is 2 feet. , The easiest way to prevent this is to check that all three lines meet at some point.
Find a corner and measure the three sides coming off of it
-- this ensures you have the right measurements.
The sides may be the same measurement.
You just want to make sure you're measuring three unique sides, even if two or three of them are all identical. , Once you've got the numbers, the rest is easy.
Simply input the measurements and add it all up.
SurfaceArea=2lw+2lh+2wh{\displaystyle SurfaceArea=2lw+2lh+2wh} SurfaceArea=2(5)(2)+2(5)(4)+2(2)(4){\displaystyle SurfaceArea=2(5)(2)+2(5)(4)+2(2)(4)} SurfaceArea=20+40+16{\displaystyle SurfaceArea=20+40+16} SurfaceArea=76{\displaystyle SurfaceArea=76} , This lets people know how you measured everything, and is a crucial part of your answer.
Luckily, all you need to do is use the units provided in the question.
For this example, since the units were in feet, you would put "feet squared" at the end of your answer:
You have a box 5 feet long, 4 feet high, and 2 feet wide, what is the total surface area? Answer: 76feet2{\displaystyle 76feet^{2}} , For example, say you had an "L" shaped box.
Instead of finding everything by hand, simply think of two separate boxes, the vertical half on top and the horizontal half on the bottom.
Find the surface area of both, then add them together to get the total surface area.For example, if you have a U shaped box:
Say the bottom has a surface area of 12 units squared.
Say both sides have a surface area of 15 units squared.
The total area would be 42 units squared, since 12+15+15=42{\displaystyle 12+15+15=42}. -
Step 3: Measure the height of the box
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Step 4: or the distance from the floor to the top.
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Step 5: Measure the width of the box.
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Step 6: Ensure that you didn't measure the same side twice.
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Step 7: Input your measurements into the formula to solve the equation.
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Step 8: Express your answer in "units squared" when done.
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Step 9: Break complex boxes into smaller pieces to find surface area.
Detailed Guide
Surface area is the total area of each side.
As long as you know how to find the area of a regular rectangle, which is simply the length times the height, you can find each side and add them together.
However, there is also a simplified formula that will do this for you if you know the measurements of the box:
SurfaceArea=2lw+2lh+2wh{\displaystyle SurfaceArea=2lw+2lh+2wh} l is the length of the box, or the longest side. h is the height of the box. w is the width of the box.
This is your longest side.
There should be 4 identical lines equally long across the whole box.
Lay the box down on it's longest side to make it easier to measure.
Example:
The length of the box is 5 feet. , Make sure you don't measure the same side as the length.
Example:
The height of the box is 4 feet. , This is the side directly perpendicular (it forms a right angle, or L) with the length.
Make sure you are not remeasuring the height.
Example:
The width of the box is 2 feet. , The easiest way to prevent this is to check that all three lines meet at some point.
Find a corner and measure the three sides coming off of it
-- this ensures you have the right measurements.
The sides may be the same measurement.
You just want to make sure you're measuring three unique sides, even if two or three of them are all identical. , Once you've got the numbers, the rest is easy.
Simply input the measurements and add it all up.
SurfaceArea=2lw+2lh+2wh{\displaystyle SurfaceArea=2lw+2lh+2wh} SurfaceArea=2(5)(2)+2(5)(4)+2(2)(4){\displaystyle SurfaceArea=2(5)(2)+2(5)(4)+2(2)(4)} SurfaceArea=20+40+16{\displaystyle SurfaceArea=20+40+16} SurfaceArea=76{\displaystyle SurfaceArea=76} , This lets people know how you measured everything, and is a crucial part of your answer.
Luckily, all you need to do is use the units provided in the question.
For this example, since the units were in feet, you would put "feet squared" at the end of your answer:
You have a box 5 feet long, 4 feet high, and 2 feet wide, what is the total surface area? Answer: 76feet2{\displaystyle 76feet^{2}} , For example, say you had an "L" shaped box.
Instead of finding everything by hand, simply think of two separate boxes, the vertical half on top and the horizontal half on the bottom.
Find the surface area of both, then add them together to get the total surface area.For example, if you have a U shaped box:
Say the bottom has a surface area of 12 units squared.
Say both sides have a surface area of 15 units squared.
The total area would be 42 units squared, since 12+15+15=42{\displaystyle 12+15+15=42}.
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Shirley Howard
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