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Perimeter of Figures

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Perimeter of Figures
Example: the perimeter of this rectangle is 7+3+7+3 = 20

Area of Triangles

The area of a triangle is always half the product of the height and base.

Example: What is the area of this triangle?

Height = h = 12
Base = b = 20
Area = ½ × b × h = ½ × 20 × 12 = 120

Volume of Rectangular Figures The volume of a rectangular prism is the length on the side times the width times the height.

Example: What is the volume of the rectangular prism with the dimension shown below?
Use the formula for the volume of a cylinder as shown below.
Volume= (2) (5) (3) = 30

Area of Irregular Figures
Without symmetry, even shape, formal arrangement

It may seem easy to find the area of a rectangle, but what if the figure has more than 4 sides?

.

The area of the first rectangle is 72 square centimeters and the area of the second rectangle is 50 square centimeters.
Together there are 72 + 50 = 122 square centimeters.
Therefore, the area of the entire figure is 122 square centimeters.

Surface Area of Rectangular Figures

Surface area is the sum of the areas of all the surfaces of a 3 – Dimensional figure.

7 m
7 m
1 m
1 m 12m 12m

S.A. = 2(1 x 7 + 12 x 7 + 12 x 1)
S.A. = 2 (7 + 84 + 12)
S.A. = 2 (103)
S.A. = 206

Determining if two ratios are proportion

If the product of the means equals the product of the extremes, then the two ratios form a true proportion. In less methyl way, cross multiply and if you get the same number both times, it is a true proportion. The top number of one ratio times the bottom number of the other.
Example
5 x 18 = 90
10 x 8 = 80 not proportion.

For 8/24 and 10/30
8 x 30 = 240 and
24 x 10 = 240 is proportional

Finding unit rates

A comparison of two measurements in which one of the terms has a value of 1.

Example
A motorcycle travels 230 miles on 4 gallons of gasoline. Find the average mileage per gallon?

For this problem, simply divide 230 by 4.

The motorcycle gets 57.5 miles per gallon.

Create/complete a table with missing values

MISSING DATA PATTERNS 1 2 3 4 5 6 7 8 9 10 HLTH x x x x CHILDS x x x x x x x x x x HAP_GEN x x x x x INCOME98 x x x x x x AGE x x x x x x x x EDUC x x x x x

Use ratio reasoning to convert measurement units

A rate is a ratio that compares two different kinds of numbers, such as miles per hour or dollars per pound.

There are 20 men and 5 women participating in a triathlon. What is the ratio of the number of women participating to the number of men participating?

Find the number of women participating and the number of men participating.

Number of women participating = 5
Number of men participating = 20

Ratio: 5:20

Finding the whole given a part and a percent

Suppose we know 13 students in Mrs. Jones’s algebra class earned Bs and that represents 37% of the class. How many students were in the class?

The 13 students represent "part" of the class. The total number of students in the class would be the "whole" class. This problem translates into "13 are 37% of what number?"

Solution

To find the "whole" we always divide the "part" by the percent. Of course we must change the percent to its decimal equivalent before completing the division. 37% is .37 in decimal form.

Since the original problem dealt with students, the answer should be rounded to the nearest whole. There were 35 students in the class.

Vocabulary for Translating Equations

Variable: A symbol (usually a letter) that represents an unknown quantity.

Constant : A value in an expression that does not change.

Algebraic Expression: An expression that contains at least one variable. It usually contains constants and opperations. Evaluate: To find the value of an algebraic expression by substituting a number for a variable.

Equation: A mathematical sentence that shows that two expressions are equal.

Solve: To find the value of the variable to make the equation true.

Isolate the Variable: To get a variable alone on one side of the equation in order to solve the equation.

Inverse Operations: Operations that undo each other; adition and subtraction, or multiplication.

Addition Property of Equality: The property that states that if you add the same number to both sides of an equation, the new equation will have the same solution.

Subtraction Property of Equality: The property that states that if you subract the same number to both sides of an equation, the new equation will have the same solution.

Multiplication Property of Equality: The property that states that if you multiply the same number to both sides of an equation, the new equation will have the same solution.

Division Property of Equality: The property that states that if you divide the same number to both sides of an equation be the nonzero number, the new equation will have the same solution.

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