CHAPTER 3 Measurement, Perimeter, Area, and Volume
CHAPTER 3 Measurement, Perimeter, Area, and Volume
3.2 Use Properties of Rectangles, Triangles, and Trapezoids
Learning Objectives
By the end of this section, you will be able to:
- Understand linear, square, and cubic measure
- Use properties of rectangles
- Use properties of triangles
- Use properties of trapezoids
Understand Linear, Square, and Cubic Measure
When you measure your height or the length of a garden hose, you use a ruler or tape measure (Figure.1). A tape measure might remind you of a line—you use it for linear measure, which measures length. Inch, foot, yard, mile, centimetre and metre are units of linear measure.
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 centimetres, or square miles to measure area. A square centimetre is a square that is one centimetre (cm) on each side. A square inch is a square that is one inch on each side (Figure.2).
Square measures have sides that are each unit in length.
(Figure.3) shows a rectangular rug that is 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.
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 centimetres. When measuring the volume of a rectangular solid, you measure how many cubes fill the container. We often use cubic centimetres, cubic inches, and cubic feet. A cubic centimetre is a cube that measures one centimetre on each side, while a cubic inch is a cube that measures one inch on each side (Figure.4).
Suppose the cube in (Figure.5) measures 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 3 inches on each side is made up of 27 one-inch cubes, or 27 cubic inches.
EXAMPLE 1
For each item, state whether you would use linear, square, or cubic measure:
a) amount of carpeting needed in a room
b) extension cord length
c) amount of sand in a sandbox
d) length of a curtain rod
e) amount of flour in a canister
f) size of the roof of a doghouse.
| a) You are measuring how much surface the carpet covers, which is the area. | square measure |
| b) You are measuring how long the extension cord is, which is the length. | linear measure |
| c) You are measuring the volume of the sand. | cubic measure |
| d) You are measuring the length of the curtain rod. | linear measure |
| e) You are measuring the volume of the flour. | cubic measure