Using Linear, Square, and Cubic Measure Appropriately
Learning Outcomes
- Given an item to measure determine whether you would use linear, square, or cubic units
- Calculate perimeter and area of a rectangle
When you measure your height or the length of a garden hose, you use a ruler or tape measure (see below). A tape measure might remind you of a line—you use it for linear measure, which measures length. Inch, foot, yard, mile, centimeter and meter are units of linear measure.
This tape measure measures inches along the top and centimeters along the bottom.
Square measures have sides that are each
unit in length.

feet long by
feet wide. Each square is
foot wide by
foot long, or
square foot. The rug is made of
squares. The area of the rug is
square feet.
The rug contains six squares of
square foot each, so the total area of the rug is
square feet.

Cubic measures have sides that are
unit in length.

inches on each side and is cut on the lines shown. How many little cubes does it contain? If we were to take the big cube apart, we would find
little cubes, with each one measuring one inch on all sides. So each little cube has a volume of
cubic inch, and the volume of the big cube is
cubic inches.
A cube that measures
inches on each side is made up of
one-inch cubes, or
cubic inches.

example
For each item, state whether you would use linear, square, or cubic measure:1. amount of carpeting needed in a room
2. extension cord length
3. amount of sand in a sandbox
4. length of a curtain rod
5. amount of flour in a canister
6. size of the roof of a doghouse.
Solution
1. You are measuring how much surface the carpet covers, which is the area. | square measure |
2. You are measuring how long the extension cord is, which is the length. | linear measure |
3. You are measuring the volume of the sand. | cubic measure |
4. You are measuring the length of the curtain rod. | linear measure |
5. You are measuring the volume of the flour. | cubic measure |
6. You are measuring the area of the roof. | square measure |
try it
Many geometry applications will involve finding the perimeter or the area of a figure. There are also many applications of perimeter and area in everyday life, so it is important to make sure you understand what they each mean.
Picture a room that needs new floor tiles. The tiles come in squares that are a foot on each side—one square foot. How many of those squares are needed to cover the floor? This is the area of the floor.
Next, think about putting new baseboard around the room, once the tiles have been laid. To figure out how many strips are needed, you must know the distance around the room. You would use a tape measure to measure the number of feet around the room. This distance is the perimeter.
Perimeter and Area
The perimeter is a measure of the distance around a figure.The area is a measure of the surface covered by a figure.
The image below shows a square tile that is
inch on each side. If an ant walked around the edge of the tile, it would walk
inches. This distance is the perimeter of the tile.
Since the tile is a square that is
inch on each side, its area is one square inch. The area of a shape is measured by determining how many square units cover the shape.
When the ant walks completely around the tile on its edge, it is tracing the perimeter of the tile. The area of the tile is
square inch.

example
Each of two square tiles is square inch. Two tiles are shown together.
1. What is the perimeter of the figure?
2. What is the area?

Show Solution
Solution
1. The perimeter is the distance around the figure. The perimeter is
inches.
2. The area is the surface covered by the figure. There are
square inch tiles so the area is
square inches.
