Circles and Area Chapter 4

4.1 Investigating Circles

INVESTIGATE

Radius Diameter

Example 1.

4.2 Circumference of a Circle

What is perimeter? What is circumference? Polygon is a figure enclosed by straight lines The distance around a polygon is called perimeter What is circumference? The distance around a circle is called circumference (C)

We already know the relationship between radius and diameter is 2r = d The relationship between diameter and circumference is very close to 3 In other words, the circumference is about 3 times the diameter (d) Therefore, to find the circumference we use

Example 1.

Example 2. Find the circumference given the following information Circle 1: Circle 2: r= 2 cm d= 24 cm

Example 3. A swimming pool has a circumference of 12 metres. Find both the radius and the diameter of the pool. (Answer to 2 decimal places)

Example 4. A circular tablecloth has diameter 1 m. The designer wants to put a fringe around the edge of the cloth. How much fringe should he buy, if fringe is sold by the tenth of a metre? Explain.

Practice Page 132 3* 6 Page 136 – 137 1* 2b*c* 4* 5 9a

Area of a Parallelogram 4.3 Area of a Parallelogram

Review from last day…

What is area and how do we find it? How would you describe a parallelogram? Which of these shapes are parallelogram? How are C and D alike? What is area and how do we find it?

INVESTIGATE 1. 3. 2.

How can we use this to find the area? Finding the area of a parallelogram We can use any side as our BASE The HEIGHT of a parallelogram is the length of a line segment that joins parallel sides! How can we use this to find the area?

We can rearrange it!

Example 1.

Example 2.

Example 3.

Practice Pages 141-142 2* 6a*b* 8* 9 10

4.4 Area of a Triangle

INVESTIGATE

Reminders** Area The amount of surface, measured in square units Triangle A polygon made up of 3 sides

How do we find the area of this rectangle? 6 3 What would the area of these triangles be?

Area of a Triangle OR

Example 1. What is the area?

Example 2. Find the area

Example 3. Find the Area

Example 4. 105 in

Practice Page 145 – 147 1* 2* 5* 6* 9 11

4.5 Area of a Circle

Review from last day

INVESTIGATE Cut the circle from the sheet and divide it into four wedges. (Cut only along the solid black lines.) Arrange the shapes so that the points of the wedges alternately point up and down Make more wedges; 8 Again, arrange the shapes for they are alternating up and down Divide it one more time so we have 16 wedges…what shape did we make? How can we connect the lengths of this parallelogram to the area of a triangle? Activity* https://illuminations.nctm.org/Lesson.aspx?id=1852

A = x radius x radius A = l x w How do we find the area of a rectangle? A = l x w So for the rectangle/parallelogram that we use our base and height… BASE = X radius HEIGHT = radius Therefore A = x radius x radius How do we write a number multiplied by itself? *Hint - E

Memorize This!!!

Example 1.

Example 2.

Example 3. The diameter of a knob on a CD player is 0.78 cm. a) What is the radius of the knob? b) What is the circumference of the knob? c) What is the area of the knob?

Example 4. A carpenter is making a circular tabletop with radius 0.5 m. What is the area of the tabletop to the nearest tenth of a metre?

Practice Page 151 – 152 1a*c* 2d* 3a* 5b* 6 8

Interpreting Circle Graphs 4.6 Interpreting Circle Graphs

Review from last class..

INVESTIGATE Answer ALL Questions

Each sector should be labeled and a percent. A circle graph compares the number in each category as well as the percent.

Some circle graphs are given a legend that we must read to find the correct information. Example 1.

Reading Graphs Example 1.

Example 2. Samson gets a raise of $500 per month. How will this affect his food budget?

Example 3.   a) Which type of program is watched for the greatest amount of time?   b) Which two types of programs are watched for approximately the same amount of time? c) Estimate the fraction of time spent watching sitcoms. d) Suppose TV is watched for 1000 days. Estimate how much time is spent watching sitcoms.

Practice Page 158 – 160 1* 3* 4a* 6 7a

4.7 Drawing Circle Graphs

Review from last class…

Percent Circles

INVESTIGATE

(Just like when you complete a full turn) Remember that all percents in a PERCENT CIRCLE must add up to 100% All of our angles in our percent circle will make a circle around the center. These angles are called central angles and should add up to 360 degrees… (Just like when you complete a full turn) These central angles can also be called sector angles

Example 1.

Example 2. The human body is made up of 20% fat, 18% bone, 50% muscle, and 12% other. Anica’s mass is 69 kg. Determine the mass of each part of Anica’s body. i) Fat ii) Bone iii) Muscle iv) Other b) Display the data on a circle graph.

Example 3.

Practice Page 163 – 164 1* 2* 4* 5