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. When you want to know how much tile is needed to cover a floor, or the size of a wall to be painted, you need to know the area, a measure of the region needed to cover a surface. Area is measured is square units. We often use square inches, square feet, square centimeters, or square miles to measure area. A square centimeter is a square that is one centimeter (cm) on each side. A square inch is a square that is one inch on each side (see below). Square measures have sides that are each [latex]1[/latex] unit in length. The next image shows a rectangular rug that is [latex]2[/latex] feet long by [latex]3[/latex] feet wide. Each square is [latex]1[/latex] foot wide by [latex]1[/latex] foot long, or [latex]1[/latex] square foot. The rug is made of [latex]6[/latex] squares. The area of the rug is [latex]6[/latex] square feet. The rug contains six squares of [latex]1[/latex] square foot each, so the total area of the rug is [latex]6[/latex] square feet. When you measure how much it takes to fill a container, such as the amount of gasoline that can fit in a tank, or the amount of medicine in a syringe, you are measuring volume. Volume is measured in cubic units such as cubic inches or cubic centimeters. When measuring the volume of a rectangular solid, you measure how many cubes fill the container. We often use cubic centimeters, cubic inches, and cubic feet. A cubic centimeter is a cube that measures one centimeter on each side, while a cubic inch is a cube that measures one inch on each side (see below). Cubic measures have sides that are [latex]1[/latex] unit in length. Suppose the cube in the image below measures [latex]3[/latex] 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 [latex]27[/latex] little cubes, with each one measuring one inch on all sides. So each little cube has a volume of [latex]1[/latex] cubic inch, and the volume of the big cube is [latex]27[/latex] cubic inches. A cube that measures [latex]3[/latex] inches on each side is made up of [latex]27[/latex] one-inch cubes, or [latex]27[/latex] cubic inches. Doing the Manipulative Mathematics activity Visualizing Area and Perimeter will help you develop a better understanding of the difference between the area of a figure and its perimeter.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. Solution1. 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 |
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[ohm_question]146501[/ohm_question]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.example
Each of two square tiles is [latex]1[/latex] square inch. Two tiles are shown together. 1. What is the perimeter of the figure? 2. What is the area?Answer: Solution 1. The perimeter is the distance around the figure. The perimeter is [latex]6[/latex] inches. 2. The area is the surface covered by the figure. There are [latex]2[/latex] square inch tiles so the area is [latex]2[/latex] square inches.
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[ohm_question]146926[/ohm_question]Licenses & Attributions
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- Question ID 146926, 146501. Authored by: Lumen Learning. License: CC BY: Attribution.
CC licensed content, Specific attribution
- Prealgebra. Provided by: OpenStax License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/[email protected].