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# Chapter 10

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## Josh Truax

on 11 March 2018

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#### Transcript of Chapter 10

Chapter 10
Section 10.1 - Areas of Parallelograms and Triangles
Base of a Parallelogram -
any one of its sides

Altitude -
segment perpendicular to the line containing that base drawn from the side opposite the base

Height -
Length of the altitude
Section 10.2 - Area of Trapezoids, Rhombuses, and Kites
Base of a Trapezoid -
either of the two parallel sides

Height of a Trapezoid -
perpendicular distance between the bases
Section 10.4 - Perimeters and Areas of Similar Figures
We can use ratios to compare the perimeters and areas of similar figures.

Theorem 10.7 - Perimeters and Areas of Similar Figures

Section 10.3 - Areas of Regular Polygons
A circle can be circumscribed around a regular polygon.

Center -
same location for both the polygon and the circle

Radius -
distance from the center to a vertex

Apothem -
perpendicular distance from the center to a side of the polygon
Section 10.6 - Circles and Arcs
Circle -
set of all points equidistant from a given point called the center
A circle is named based on its center
Section 10.5 - Trigonometry and Area
We have already learned how to find the area of a regular polygon:

A = 1/2 a p
Area
Theorem 10.1 - Area of a Rectangle
The area of a rectangle is the product of its base and height.
A = b · h
Theorem 10.2 - Area of a Parallelogram
The area of a parallelogram is the product of a base and the corresponding height.
A = b · h
Base of a Triangle -
any one of the three sides

Height -
length of the altitude to the line containing the base
Theorem 10.3 - Area of a Triangle
The area of a triangle is half the product of a base and the corresponding height.
A = 1/2 b · h
Find the area of the following rectangle
24 in
11 in
Find the area of the parallelogram
8 ft
13 ft
10 ft
Find the area of the triangle
3 mm
4 mm
8 mm
Find the total area
6 m
18 m
8 m
12 m
Homework #14 - Section 10.1
Complete the assignment on Math XL.

**Remember!!! You must complete 100% of the assignment in order to earn full credit in the grade book.***
Theorem 10.4 - Area of a Trapezoid
The area of a trapezoid is half the product of the height and the sum of the two bases.
Theorem 10.5 - Area of a Rhombus/Kite
The area of a rhombus or a kite is half the product of the lengths of its diagonals.
Find the area of the trapezoid
30 mm
8 mm
48 mm
Find the area of the kite
3 cm
3 cm
5 cm
12 cm
Find the area of the trapezoid
Find the area of the rhombus
Homework #15 - Section 10.2
Complete the assignment on Math XL.

**Remember!!! You must complete 100% of the assignment in order to earn full credit in the grade book.***
Finding Angle Measures in a Regular Polygon
Since all of the polygons we will encounter in this chapter are regular polygons, we know the angle measures inside of the polygons will always be congruent.

Thus, when finding the angle measures around the center of the polygon, we take 360 and divide it by the total number of sides.

This gives us the measure of each individual angle
Find the measure of each numbered angle
Theorem 10.6 - Area of a Regular Polygon
The area of a regular polygon is half the product of the apothem and the perimeter.
Find the area of the regular decagon
Find the area of the regular hexagon
Find the area of the square
Homework #16 - Section 10.3
Complete the assignment on Math XL.

**Remember!!! You must complete 100% of the assignment in order to earn full credit in the grade book.***
The trapezoids are similar. Find the following
1) Their scale factor
2) The ratio of their perimeters
3) The ratio of their areas
The area of the smaller pentagon is 27.5 cm. What is the area of the larger pentagon?
2
What is the ratio of the
perimeters
between the two triangles?
The
scale factor
of the dimensions of two similar wood floors is
4:3
. It costs \$216 to clean the smaller wood floor.

How much would it cost to clean the larger wood floor?
Homework #17 - Section 10.4
Complete the assignment on Math XL.

**Remember!!! You must complete 100% of the assignment in order to earn full credit in the grade book.***
.
So far, we have used the rules of 30-60-90 triangles and 45-45-90 triangles to help us solve.
There will be times when we have to use the rules of sin/cos/tan to solve.
Find the area
Theorem 10.8 - Area of a Triangle Given SAS
The area of a triangle is half the product of the lengths of the two sides and the sine of the included angle.
Find the area
Find the area
Homework #18 - Section 10.5
Complete the assignment on Math XL.

**Remember!!! You must complete 100% of the assignment in order to earn full credit in the grade book.***
Section 10.7 - Areas of Circles and Sectors
Theorem 10.11 - Area of a Circle
T
Circle T
Diameter -
segment that contains the center of a circle and has both endpoints on the circle

Radius -
segment that has one endpoint on the center and one endpoint on the circle
*Half the length of the diameter

Central Angle -
angle whose vertex is the center of the circle

Congruent Circles -
have congruent radii
Semicircle -
half of a circle (180°)

Minor arc -
less than a semicircle; named using two points (less than 180°)

Major Arc -
larger than a semicircle; named using three points (greater than 180°)
Name the following:
3 minor arcs
3 major arcs
3 semicircles
Arc Measure
The measure of a
minor arc
is equal to its corresponding central angle.

The measure of a
major arc
is the measure of the related minor arc subtracted from 360.

The measure of a
semicircle
is 180°.

Adjacent Arcs
share a common point.
Postulate 10.2 - Arc Addition Postulate
The measure of the arc formed by two adjacent arcs is equal to the sum of the measures of the two arcs.
Find the measure of the following arcs
Circumference -
the distance around a circle

Pi ( ) -
the ratio of the circumference of a circle to its diameter
Theorem 10.9 - Circumference of a Circle
The circumference of a circle is pi times the diameter.
Find the circumference. Leave your answer in terms of pi.
Theorem 10.10 - Arc Length
The length of an arc of a circle is the product of the ratio measure of the arc and the

circumference of the circle.
360
Find the length of the red arc.
Homework #19 - Section 10.6
Complete the assignment on Math XL.

**Remember!!! You must complete 100% of the assignment in order to earn full credit in the grade book.***
The area of a circle is the product of pi and the square of the radius.
Find the area of each circle. Leave your answer in terms of pi.
Sector of a Circle -
region bounded by an arc of the circle and the two radii to the arc's endpoints.
Think a slice of pizza
Theorem 10.12 - Area of the Sector of a Circle
The area of a sector of a circle is the product of the ratio measure of the arc and the area of the circle.
360
Find the area of the shaded sector.

Leave your answer in terms of pi.
Segment of a Circle -
a part of a circle bounded by an arc and the segment joining its endpoints.
Think the crust in a slice of pizza
Area of a Segment
Find the area of the shaded segment.

Round your answer to the nearest tenth.
Find the area of the shaded region. Round your answer to the nearest tenth.
Homework #20 - Section 10.7
Complete the assignment on Math XL.

**Remember!!! You must complete 100% of the assignment in order to earn full credit in the grade book.***
Notebook Question #1
Notebook Question #2
Notebook Question #3
Notebook Question #4
Notebook Question #1
Notebook Question #2
Notebook Question #3
Notebook Question #4
Notebook Question #1
Notebook Question #2
Notebook Question #3
Notebook Question #4
Notebook Question #1
Notebook Question #2
Notebook Question #3
Notebook Question #4
Notebook Question #1
Find the area
Notebook Question #2
Notebook Question #3
Notebook Question #4
Notebook Question #1
Notebook Question #2
Notebook Question #3
Notebook Question #4
Notebook Question #1
Notebook Question #2
Notebook Question #3
Notebook Question #4
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