What is Surface Area?
Let’s cover the surfaces of some three-dimensional objects.
12.1: Covering the Cabinet (Part 1)
Your teacher will show you a video about a cabinet or some pictures of it.
Estimate an answer to the question: How many sticky notes would it take to cover the cabinet, excluding the bottom?
12.2: Covering the Cabinet (Part 2)
Earlier, you learned about a cabinet being covered with sticky notes.
- How could you find the actual number of sticky notes it will take to cover the cabinet, excluding the bottom? What information would you need to know?
- Use the information you have to find the number of sticky notes to cover the cabinet. Show your reasoning.
How many sticky notes are needed to cover the outside of 2 cabinets pushed together (including the bottom)? What about 3 cabinets? 20 cabinets?
12.3: Building with Snap Cubes
Here is a rectangular prism built from 12 cubes:
It has six faces, but you can only see three of them in the sketch. It has a surface area of 32 square units.
The applet has 12 blocks, too. They are all in the same spot on the screen, like a hidden stack of blocks. You will always know where the stack is because it sits on a gray square. To use a block, drag the red point to move it. Click on the red points to change from left/right movement to up/down movement.
Use all 12 cubes to build a different rectangular prism (with different edge lengths than shown in the prism here). You can turn the view to see all of the faces of your figure.
- How many faces does your figure have?
- What is the surface area of your figure in square units?
- The surface area of a figure (in square units) is the number of unit squares it takes to cover the entire surface without gaps or overlaps.
- If a three-dimensional figure has flat sides, the sides are called faces.
- The surface area is the total of the areas of the faces.
For example, a rectangular prism has six faces. The surface area of the prism is the total of the areas of the six rectangular faces.
So the surface area of a rectangular prism that has edge-lengths 2 cm, 3 cm, and 4 cm has a surface area of \(\displaystyle (2\boldcdot 3)+ (2\boldcdot 3) + (2\boldcdot 4) + (2\boldcdot 4) + (3\boldcdot 4) + (3\boldcdot 4)\) or 52 square centimeters.
Each flat side of a polyhedron is called a face. For example, a cube has 6 faces, and they are all squares.
- surface area
The surface area of a polyhedron is the number of square units that covers all the faces of the polyhedron, without any gaps or overlaps.
For example, if the faces of a cube each have an area of 9 cm2, then the surface area of the cube is \(6 \boldcdot 9\), or 54 cm2.