Notes for the 4th Grading period

1
Notes for the 4th Grading period

• Mrs. Neal
• 6th Advance and 7th Average

2
Section 11.5 Area of Triangles and Trapezoids

• Objective
• To find the areas of triangles and trapezoids
• Vocabulary
• 1. Trapezoid - quadrilateral with one pair of
  parallel sides.
• Area of a triangle A 1 x b x h or b x h
• area .5 x base x height 2 2
• A .5x3x7
• A 10.5 cm sq

height
3cm
7 cm
base
3
Section 11.5 Area of Triangles and Trapezoids
Base 1

• Area of a trapezoid
• expressed in square units
• A .5h(b 1 b 2)
• or h (b1 b2)
• 2
• A .5 x 5 (8 12 )
• A .5 x 5 ( 20 )
• A .5 x 100
• A 50 in squared

hheight
Base 2
8in
5 in
12in
4
Section 11.7 Area of Complex Figures

• Objective To find the areas of complex figures
• Vocabulary
• 1. Complex Figure a figure made p of circles,
  rectangles, squares and other 2 dimensional
  figures.
• To find the area of complex figures, separate it
  into figures you already know how to find the
  areas of and then add the numbers together.

5
Section 11.7 Area of Complex Figures

• take the area of the rectangle
• and the triangle separately
• then add the areas together
• rectangle length 6ft
• width 3ft
• Area 6 x 3 18 ft sq
• triangle base 2ft
• height 1ft
• Area .5 x 2 x 1 1 ft sq
• Rectangle area triangle area 18 1 19 ft
  sq (total)

6ft
3ft
4ft
2ft
6
Section 11.7 Area of Complex Figures

• Find the area of circle and divide in
  half
• Area 3.14 x r 2
• Area 3.14 x 11 2
• 3.14 x 121
• 379.9 m sq.
• then divide in half
• 379.9 189.95 m sq.
• 2

7
Section 11.7 Area of Complex Figures

• The pitching mound on a baseball field has a
  circular area of 254.47 square feet. Find its
  diameter. Round to the nearest foot.
• Work backward through the problem
• Area 3.14 x r 2 so 254.47 3.14 x r 2
• 254.47 r 2
• 3.14
• 81.04 r 2
• v81.04 r
• 9 r
• d 2r 2x9 18
• So the diameter of the pitchers mound is 18 ft

8
Section 12.2 Volume of Rectangular Prisms

• Objective
• To find the volume of rectangular prisms
• Vocabulary
• 1. Volume- the measure of space inside of a three
  dimensional figure. It is measured in cubic units
  (meaning the units are raised to the third power
  unlike area which is to the second power)
• Formula- V L x W x H
• Volume Length x Width x Height

9
Section 12.2 Volume of Rectangular Prisms

• 2. Rectangular Prism a solid figure that has
  two parallel and congruent sides, or bases, that
  are rectangles.
• Volume 5 x 8 x 3 120 cm 3

3cm
5cm
8cm
10
12.3 Volume of Cylinders

• Objective
• To find the volume of cylinders
• Vocabulary
• 1. Cylinder a solid figure that has two
  congruent, parallel circles are its bases.
• Formula pi x r 2 x h 3.14 x r 2 x h
• V 3.14 x 3 2 x 7
• V 3.14 x 9 x 7
• V 3.14 x 63 197.82
• 197.8 in 3

3in
7in
11
12.4 Surface Area of Rectangular Prisms

• Objective
• To find the surface areas of rectangular prisms
• Vocabulary
• Surface area the sum of all of the areas, or
  faces, of a three-dimensional figure
• Formula SA 2lw 2lh 2wh

12
12.4 Surface Area of Rectangular Prisms

• Ex.

3cm
4cm
5cm
L5 w4 h3 SA 2x5x4 2x5x3 2x4x3 SA 40
30 24 SA 94 cm 2
13
12.4 Surface Area of Rectangular Prisms

• L7in W 2in H 9in
• SA 2x7x2 2x7x9 2x2x9
• SA 28 126 36
• SA 190in2

14
12.5 Surface Area of Cylinders

• Objective
• To find the surface areas of cylinders
• Vocabulary
• Circumference the distance around a circle
• Formula
• SA 2x(3.14xr2) (2x3.14xr)xh
• The area of two circles circumference of base
  times the
• height

15
12.5 Surface Area of Cylinders
A 3.14xr 2 3.14 x 4 2 50.2 in sq
R 4in
H 2in
A 2x3.14xrxh 2x3.14x4x2 157.8
in sq
A 3.14xr 2 3.14 x 4 2 50.2 in sq
SA 2(50.2) 157.8 100.5 157.8
258.3in sq
16
7-1 Ratios

• Ratios a comparison of two numbers by division
• Equivalent Ratios 2 ratios that have the same
  value
• Can be written in several different ways
• 28 or 2/8 or 2 to 8
• Can also be simplified
• Best way- treat as a fraction and reduce to
  lowest terms
• Can not compare numbers in a ratio unless they
  have the same unit, if not you must convert one
  unit to the other.
• Examples
• 1. 9 to 12 9/12 ¾
• 2. 2715 27/15 9/5
• 3. 4 feet4 yards 4 feet 12 feet 4/12
  1/3

17
7-1 Ratios

• Comparisons of two ratios
• 3/8 compared to 6/12
• Turn into decimals
• .375 and .5
• So 6/12 is greater

18
7-2 Rates

• Rate a ratio that compares 2 quantities with
  different kinds of units
• Unit rate a rate simplified to a denominator of
  1 unit
• Examples
• 1. rate300 tickets in 6 days
• Unit rate50 tickets in 1 day
• 2. rate220miles on 8 gallons
• Unit rate 27.5 miles on 1 gallon

19
7-2 Rates

• Comparison of rates which is the better buy?
• 8 oz jar of pickles for 1.14 or a 12 oz jar for
  1.75?
• 1.12/8 0.14 per oz
• 1.75/12 0.15 per oz
• 8 oz jar is the better buy

20
7-3 Solving Proportions

• Proportion an equation stating two ratios are
  equivalent
• Cross product- the product of the numerator of
  one ratio and the denominator of the other ratio.
  If equal-then it is a proportion
• Cross multiply and divide is the method of
  finding a missing number in a proportion.

21
7-3 Solving Proportions

• Do these ratios form a proportion?
• 1. 4/9 and 2/3
• cross products 4x312 and 9x218
• Cross products not equal therefore not a
  proportion
• 2. 15/9 and 10/6
• Cross products 15x690 and 9x1090
• Cross products are equal therefore it is a
  proportion
• Solve the proportion
• 3. 1/5 x/60 1x605x12
• 4. 10/k2.5/4 10x42.5 k16

22
10-6 Similar Figures

• Similar Figures figures that have the same
  shape but not necessarily the same size.
• Indirect Measurement-when you use similar figures
  to find the length, width, or height of objects
  too difficult to measure directly.
• Solving method use a proportion take the
  given measurements of one figure and set it equal
  to the given and missing measurements of the
  other figure.

5/15 4/x 5x415x X12m
6m
18m
5m
15m
4m
x
23
10-6 Similar Figures

• 7/8x/1.5
• 7x1.58x
• X1.3 cm

7cm
x
1.5cm
8cm
24
7-4 Scale Drawings

• 7-4 Scale Drawings
• Scale Drawings - a drawing that represents
  something too small or too large to be drawn at
  actual size.
• Scale - gives the relationship between the
  distance between the distance on the map and the
  actual distance.
• Scale Factor a scale written as a ratio in
  simplest form with the same units
• Ex. 1cm 2.5 m - scale factor is 1cm 250 cm
  ( 100 cm in 1 meter)

25
7-4 Scale Drawings

• Scale model a model used to represent something
  that is too small or too large for an actual
  sized model (cell in the body, layout of a city)
• Method to solve set up as a proportion and
  solve for missing number. Use the given scale as
  the first fraction.
• Ex. The distance from a city in Indiana to
  another city in Illinois is 8cm on a map. If the
  scale factor of the map is 1cm 25km, find the
  actual distance between the cities.
• 1/25 8/a so 25 x 8 a 200 km as the actual
  distance.

26
7-7,7-8,8-2 Percent Proportion

• 7-8 Percent Proportion
• 7-7 Percent of a number
• 8-2 Percent Equation
• All of these sections measure the same thing
• Uses proportion set-up to find a missing number
• Percent Proportion compares a part of a
  quantity to the whole quantity (base)
• /100 is /of or /100 part/base

27
7-7,7-8,8-2 Percent Proportion

• Usually the number that is the part has the word
  (is) in front of it and the number that is a base
  has the word (of) in front of it.
• The number 100 is always in the proportion and
  the percent number is always on top of the 100.
• Solve by cross multiplying then dividing to find
  the missing number.
• Ex. 52 of 160 52/100 ?/160 so 52 x 160
  100 83.2
• Ex. What percent of 60 is 15 ?/100 15/60 so
  15 x 100 60 25

28
8-4 Percent of Change

• Percent of change a ratio that compares the
  change in quantity to the original amount
• Equation percent of change amount of change
• original amount
• Percent of increase if the original quantity is
  increased
• Percent of decrease if the original quantity is
  decreased
• Method of solving find the difference between
  the new and original measures or amounts, this
  number is the numerator and the original number
  is the denominator. Divide the difference by the
  original then multiply by 100 to make it a
  percent. Then identify it as a decrease or a
  increase

29
8-4 Percent of Change

• Examples
• Original 75
• New 15 75-15 60 then 60/75 .8
• then .8 x 100 80 decrease since the
  price went down
• Last year the chess club had 24 members. This
  year the club has 30 members. Find the percent of
  decrease in the number of members.
• 30-24 6 then 6/30 .2
• then .2 x 100 20 increase since the
  membership went up.

30
8-5 Sales Tax and Discount

• Sales tax an additional amount of money charged
  on items that people buy. The total cost of an
  item is the regular price plus the sales tax
• Discount the amount by which the regular price
  of an item is reduced. The sale price is the
  regular price minus the discount.
• Examples
• Sales tax graphing calculator costs 90,
• sales tax 4.25
• find what 4.25 of 90 is .0425 x 90 3.83
• then add it to 90 90 3.83 93.83

31
8-5 Sales Tax and Discount

• Sales tax socks 2.99 sales tax 5.5
• .055 x 2.99 .16
• 2.99 .16 3.15
• Discount snowboard 169 on sale 35 discount
  
• .35 x 169 59.15
• 169 59.15 109.85
• Percent of discount - guitar original price
  299.95
• new price 179.99
• 299.95-179.99119.96 then 119.96299.95 .399
  .40
• .40 x 100 40