Surface Area

​Surface Area

By Ashley Moser

The images below show a cabinet and a person placing a single sticky note on the front of the cabinet. Examine the images. Consider how many sticky notes it might take to cover the cabinet, not including the bottom.

Poll

What is a good estimate of the number of sticky notes needed to cover the 5 sides?

• 601 to 901

• 301 to 600

• 0 to 300

Examine the images of the cabinet. Use them to help you think about how to find a more accurate count of sticky notes to cover all five surfaces.

Reflect on some ideas before moving on.

The cabinet has five sides showing the front, back, left, right, and top, which will all be covered in sticky notes.

Sides

Notice, the shape of the sides and top of the cabinet are all rectangles.

Shapes

The back of the cabinet is 12 sticky notes wide.

The height, length, and width of the cabinet in terms of sticky notes is 24 by 12 by 6.

Dimensions

Multiple Choice

Which strategy could you use to find the actual number of sticky notes it will take to cover the cabinet, excluding the bottom?

Think about each strategy in terms of sticky notes.

• Find the area of each rectangular side of the cabinet, excluding the bottom, and add them together.

• Find the perimeter of each rectangular side, excluding rectangular bottom, then add them together.

• 
  Find the area of one side of the cabinet, then multiply by five because there are five sides.

Recall the dimensions of the cabinet in terms of sticky notes:

• front and back: 12 by 24

• left and right: 6 by 24

• top: 6 by 12.

Notice that the front of the cabinet has handles that will not be covered in sticky notes. Two handles are the size of one whole sticky note and it needs to be removed from your calculation.

Draw

Calculate the number of sticky notes needed to cover the cabinet.

Multiple Choice

What is the actual number of sticky notes it will take to cover the cabinet, excluding the bottom and the handles?

• 935

• 863

• 1727

​Each flat side of this box is called a face. In this figure, there are 6 rectangular faces.

The surface area of a three-dimensional figure is the number of square units that cover all the faces of the figure, without gaps or overlaps.

The surface area is the sum of the area of each face, and it is measured in square units such as square inches or square meters.

Multiple Choice

How many faces does this figure have?

• 6

• 4

• 8

​A three-dimensional rectangular figure built from 12 cubes is shown to the right. It has six faces, but you can only see three of them in the image.

This figure has dimensions of 2 units by 2 units by 3 units. Count the individual squares made by the counting cube faces on all faces of your block.

Draw

Create your own 3D figure. then, count the dimensions to find the surface area.

Match

Here are the dimensions of the figures your teammates built. What is the surface area for each figure?

Match the dimensions to their surface areas. You may wish to create these rectangular figures using your cubes or draw the rectangular sides to help.

• 
  

  1 by 1 by 12

• 1 by 2 by 6

• 2 by 3 by 4

• 3 by 3 by 3

• 2 by 2 by 5

50 sq units

24 sq units

30 sq units

27 sq units

28 sq units

• 50 sq units

• 24 sq units

• 30 sq units

• 27 sq units

• 28 sq units

​To summarize the important key concepts of this lesson:

• The surface area of a figure 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.

Open Ended

How are finding surface area and finding area alike? How are they different?

You can start your response with:

• Finding surface area and finding area are alike because . . .

• Finding surface area and finding area are different because . . .

Multiple Choice

The rectangular figure shown is 3 units high, 2 units wide, and 5 units long. What is its surface area in square units?

• 62 sq units

• 70 sq units

• 30 sq units

Multiple Choice

What is the surface area in square units of this rectangular figure?

• 48 sq units

• 54 sq units

• 52 sq units

Hotspot

Which figure has a surface area of 22 sq units?

Multiple Choice

What is the surface area in square units of this rectangular figure?

• 72 sq units

• 32 sq units

• 64 sq units

Hotspot

A rectangular figure is 4 units high, 2 units wide, and 6 units long. What is the surface area in square units?

Multiple Choice

Which description can represent the surface area of this trunk?

• the number of square feet that cover the entire outside faces of the trunk

• the number of square inches that cover the top of the trunk

• the number of cubic inches of horizontal surface inside the trunk