Chapter 10 Notes Packet
Notes #7-Sections 10.1 & Section 1.9
Perimeter of a Rectangle & ParallelogramFormula: / Example: Find the perimeter of the parallelogram.
Area of a Rectangle, Square, & Parallelogram
Formula: / Example: Find the area of the parallelogram.
Circumference of a Circle
Formula: / Example: Find the circumference of the circle.
Area of a Circle
Formula: / Example: Find the area of the circle.
Area of a Triangle:
Formula: / Example: Find the area of the triangle.
Examples: Find the area of each figure.
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/ 2.)
3.)
/ 4.)
Examples: Find the perimeter of the rectangles or squares & the circumference of the circles.
5.)/ 6.)
7.)
/ 8.)
Examples: Find the area of each figure.
9.)/ 10.)
11.)
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Examples: Word Problems. Draw a diagram & set up an equation to solve each word problem.
13.) The area of a triangle is and the base of the triangle is 18 ft. Find the height of the triangle. / 14.) The perimeter of a rectangle is 40 cm. The length of the rectangle is 8 cm. Find the height of the rectangle.15.) The area of a parallelogram is 84 and the height is 4 inches. Find the base of the parallelogram. / 16.) An isosceles right triangle has an area of
162 . Find the length of each leg.
Algebra Review: Exponent Rules
Multiplying Terms with the Same Base:
Examples: Simplify each expression as much as possible.
17.) / 18.)19.) / 20.)
Notes #8-Section 10.2
Formula: / Example:
1.) Find the area of the trapezoid
Area of a Rhombus
Formula: / Example:
2.) Find the area of the rhombus.
Examples: Find the area of each trapezoid. If your answer is not an integer, leave it in simplest radical form.
3.)/ 4.)
5.)
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7.)
Examples: Find the area of each rhombus.
8.) rhombus/ 9.) rhombus
10.)
/ 11.) rhombus
Examples: Word Problems. Draw a diagram & set up an equation to solve each word problem.
12.) The area of a trapezoid is when the two bases have measures of 4 inches and 10 inches. Find the height of the trapezoid. / 13.) The perimeter of a rhombus is 40 yd and one diagonal is 16 yd. Find the length of the 2nd diagonal & then find the area of the rhombus.14.) Find the area of a rhombus whose sides are 29 mm each and has one diagonal of length 42 mm.
Algebra Review: Exponent Rules
Power to a Power: Product to a Power:
Examples: Simplify each expression as much as possible.
15.) / 16.)17.) / 18.)
Notes #9—Section 10.3
Common Examples:
Square Equilateral Triangle Regular Hexagon
Key Info:
apothem (a) = distance from ______radius (r) = distance from ______
to ______to ______
Area of a Regular Polygon
Find the missing information:
/ 1.)
/ 2.)
/ 3.)
/ 4.)
/ 5.)
/ 6.)
Example: Find the area of each figure below.
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9.)
/ 10.)
Algebra Review: Exponent Rules
Dividing Terms with the Same Base:
Examples: Simplify each expression as much as possible.
11.) / 12.)13.) / 14.)
Notes #10—Section 10.4
Perimeters & Areas of Similar Figures:
If the scale factor of two similar figures is , then:
· The ratio of their perimeters or circumferences is
· The ratio of their areas is
Complete the table referring to similar figures:
#1 / #2 / #3 / #4 / #5 / #6Scale Factor / 1:3 / 4:5
Ratio of bases / 2:3
Ratio of perimeters / x:y
Ratio of areas / 4:49 / 25:64
7.) The areas of two similar triangles are 50m2 and 32m2. What is the ratio of their bases? / 8.) The diameters of two circles are 12in and 15in. What is the ratio of their areas?
9.) The scale factor of two similar polygons is 2:3.
a) If the base of the smaller polygon is 8m, find the base of the larger polygon. / b) If the area of the larger polygon is 45m2, find the area of the smaller polygon.
Notes #11—Sections 10.1-10.4 Review
1.) The perimeters of two similar rectangles are 20m and 30m.a) What is the ratio of their lengths?
b) What is the ratio of their areas? / 2.) The areas of two circles are and .
a) What is the ratio of their areas?
b) What is the ratio of their circumferences?
3.) The scale factor of two similar figures is 4:7.
a) What is the ratio of their areas?
b) If the area of the smaller figure is 64ft2, what is the area of the larger figure? / 4.) The areas of two similar figures are 98cm2 and 72cm2.
a) What is the ratio of their areas?
b) What is the ratio of their perimeters?
c) If the perimeter of the smaller figure is 24cm, what is the perimeter of the larger figure?
5.) Find the area of a square with radius 9ft. / 6.) Find the area of a regular hexagon with perimeter 120m.
7.) Find the area of an equilateral triangle with apothem 11cm. / 8.) Find the area of a rhombus whose perimeter is 104 cm and where one diagonal is 20 cm.
9.) The area of a trapezoid is 48 yd. The height is 3 yd and the larger base is four more than the shorter base. Find the lengths of the two bases.
Notes #12—Section 10.6
A semicircle is… / Picture:
A minor arc is… / Picture:
A major arc is… / Picture:
Adjacent arcs are… / Picture:
Examples: In , are diameters. Identify the following.
1.) two major arcs
2.) two minor arcs /
3.) two semicircles / 4.) a pair of adjacent arcs
5.) an acute central angle / 6.) an obtuse central angle
Examples: Find the measure of each arc in .
7.)
8.) /
9.) / 10.)
11.) / 12.)
Arc Addition Postulate
In Words:
The measure of the arc formed by ______arcs is the ______of the measures of the two arcs. / 13.) Find the value of x given that .
Arc length is… / Formula for Arc Length:
Examples: Find the length of each arc shown in blue. Leave your answer in terms of .
14.)/ 15.)
16.)
/ 17.)
Algebra Review: Exponent Review
Zero Exponents:
Examples: Simplify each expression as much as possible.
18.) / 19.)20.) / 21.)
Notes #13-Section 10.7
A sector of a circle is… / Picture:Area of a Sector of a Circle
Examples: Find the area of each shaded sector of a circle. Leave your answer in terms of .
1.)/ 2.)
3.)
/ 4.)
A segment of a circle is part of a circle bounded by an ______and the ______joining the ______. / Picture:
Area of segment = Area of sector – Area of triangle
Examples: Find the area of each shaded segment. Round your answer to the nearest tenth or leave your answer with reduced fractions & radicals.
5.)/ 6.)
7.)
/ 8.)
HW #14--Chapter 10 Study Guide Name: Per.
Please show all of your work! NO WORK = NO CREDIT! You may ONLY use a calculator on the problems where you see “CALCULATOR OK” next to them!!
For #1-16, find the area of each figure. Do not round your answers. If needed, leave in your answer. Don’t forget about your units!!1.)
/ 2.)
3.)
/ 4.)
5.) A rectangle has a diagonal of 13 in. and one side of 5 in. Find the area of the rectangle. / 6.) The perimeter of a rhombus is 20 cm and one diagonal is 8 cm. Find the area of the rhombus.
7.) A circle has a circumference of yd. Find the area of the circle. / 8.) A trapezoid has a median of 16 m and a height of 4 m. Find the area of the trapezoid.
9.)
/ 10.) A regular hexagon with perimeter 60 in.
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15.) An equilateral triangle with apothem 10 yd. / 16.) A regular dodecagon with a side of length 6 in and an apothem of 5 in.
For #17-22, use the circle at the right. In are diameters. Identify the following.
17.) two minor arcs
18.) two major arcs /
19.) two semicircles / 20.) a pair of adjacent arcs
21.) an acute central angle / 22.) an obtuse central angle
For #23-25, find the measure of each arc in .
23.) 24.)
25.) /
For #26-27, find the length of each arc.
26.)
/ 27.)
For #28-29, find the area of each shaded sector of a circle. Leave your answers in terms of .
28.)
/ 29.)
For #30-31, find the area of the shaded region. Round your answers to the nearest tenth or with reduced radicals.
30.) CALCULATOR OK.
/ 31.) CALCULATOR OK.
For #32-35, simplify each expression as much as possible using your exponent rules. Do not leave any negative exponents in your answers!
32.) / 33.)
34.) / 35.)
36.) The scale factor of two similar polygons is 2:7. What is the ratio of:
a) their corresponding sides?
b) their perimeters?
c) their areas? / 37.) The scale factor of two similar polygons is 3:5. The area of the larger polygon is 75m2. Find the area of the smaller polygon.
38.) The areas of two regular hexagons are 9cm2
and 25cm2. What is the:
a) ratio of their sides?
b) ratio of their perimeters? / 39.) The perimeters of two similar parallelograms are 4m and 8m. What is the:
a) scale factor?
b) ratio of their areas?