Page 1 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

1

UNIT 11

Angle Relationships, Area, and

Perimeter/Circumference

CCM6

Name: ________________

Math Teacher:___________

Projected Test Date:_____

MAIN IDEAS PAGE(s)

Unit 11 Vocabulary 2

Perimeter of regular/ irregular figures (including missing dimensions) 3-6 Area of squares, rectangles, parallelograms, triangles and trapezoids (including missing dimensions)

7-15

Composite and Inscribed figures 16-24 Area and Perimeter on the Coordinate Plane 25-29

STUDY GUIDE 30-33

Page 2 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

2

Unit 11 Vocabulary

perimeter the measure around an object

area the amount of space inside a figure

polygon a closed plane figure formed by 3 or more line segments that intersect only at their endpoints

regular polygon a figure that has all equivalent sides and angles

rectangle a parallelogram with four right angles

triangle a 3-sided polygon

hypotenuse the longest side of a right triangle

parallelogram a four sided figure with opposite sides that are equal and parallel

Page 3 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

3

Perimeter and Area

WARMUP: Answer the two questions and fill in the chart below. Complete this page and the next two.

Mr. Bill’s backyard is in the shape of a rectangle. It took him 600 feet of

fence to enclose his back yard. If the length of the yard is twice as long as the

width, what are the dimensions of Mr. Bill’s yard?

The Brown family has a square back yard with an area of 25 meters squared.

They need to put a fence around it for their dog. How long will the fence be?

Now, complete all you can on the next page.

Page 4 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

4

Page 5 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

5

PERIMETER REVIEW

What is it? How do I calculate it?

PERIMETER

AREA

Find the Perimeter of each shape below.

Find the length of the missing side if given the Perimeter of the whole shape.

If the perimeter of a regular

hexagon is 30cm, what is the

length of one side?

Page 6 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

6

Page 7 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

7

Perimeter Review, Area of Polygons

The Relationship between Rectangles and Triangles

Page 8 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

8

Calculating Area of Squares/Rectangles/Parallelograms

A parallelogram is just a

______________ in disguise!

SHOW IT!

Area formulas you need to KNOW:

Shape Formula Example Solved Together Your Turn

Square

AREA=_______________

AREA=______________________

Rectangle

AREA=________________

AREA=__________________

Parallelogram

AREA=__________________

AREA=_________________

Page 9 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

9

WHAT BIG IDEA DO YOU NOTICE WITH TRIANGLES?________________________________________________

Page 10 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

10

On your calculator, type

APPS

Choose AreaForm

Press any key twice

Choose #1

Choose 3: Parallelogram

After it defines the parallelogram, click the WINDOW key to see the area formula.

When it finishes telling the formula, click the GRAPH key to see “Why?” Click GRAPH again.

Do it again with #4: Triangle and check out #5 Trapezoid. **You don’t have to “know” trapezoids.

Here are two right triangles: Here are two non-right triangles:

What shape do these create together? What shape do these create together?

EVERY TRIANGLE DOUBLED MAKES EITHER A _____________________ or a __________________________.

Since a _________________________ is really a tilted ______________________ (same area), the area of a

triangle is always __________ of the area of a ____________________ or a _____________________.

FORMULA FOR THE AREA OF A TRIANGLE:

A = ____________(_____________• ______________)

Find the Area of each shape:

Page 11 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

11

REVIEW of AREA of TRIANGLES and PARALLELOGRAMS

How do I find the area of a

parallelogram?

Area = base x height

Since a parallelogram is similar to a rectangle, the

base and height are relative to the length and

width.

* Be careful to measure the height – and NOT the

length of the slanted side.

Parallelogram and its relation to a

rectangle:

(teachers: Demonstrate this using a

piece of paper)

Notice that when the outside piece is cut off and

pasted to the other side of the parallelogram –

the polygon that is formed is a rectangle.

Practice:

B = 2.5 ft

Area = bh

Area = 2.5 x 1.25

Area = 3.125 square ft

* remember to label with square units, because

this is a two dimensional figure.

Practice:

4.5 ft

12 ft

Area = bh

Area = 12 x 4 Area = 48 square feet.

H= 1.25 ft

4ft

Page 12 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

12

Practice:

A parallelogram has these measures:

Base = 4.1 inches

Height = 2.2 inches

Answer: 9.02 square inches

Practice:

A parallelogram has these measures:

Base = 4 yd

Height = 9 yd

Answer: 36

How do I find the area of a triangle? Look at this rectangle –

When I split the rectangle in half – what shapes

are formed?

Two triangles are formed when a rectangle is split

in half. So, half of a rectangle is a triangle. So,

half of the area of a rectangle is a triangle.

Therefore,

Area of a triangle = 2

1bh

NOTE: Multiplying by

2

1 is the same as dividing by 2. You

may see or use the formula like this: 2

bh

Example:

H = 10.5 m

B= 16.8 m

Area = ½ bh

Area = 0.5 x 16.8 x 10.5 =

Area = 88.2 sq. m or 88.2 m2

*Remember – this is still a two dimensional figure –

therefore your answer should be labeled in square

units.

Page 13 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

13

Practice:

B = 6 cm

Area = ½ bh

Practice:

The base of a triangle is 3 m and the

height is 8 sq. m. What is the area?

Start by writing the formula, then substituting for

what you know.

A =

Practice:

The base of a triangle is 8 cm and the

area is 32 cm. What is the height of

the triangle? (You will have to

rearrange the formula)

Start by writing the formula, then substituting for

what you know.

A =

H= 11 cm

Page 14 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

14

HOMEWORK Day 2

Page 15 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

15

Area of Trapezoids

On your TI-73, use the AREAFORM application and watch the area formula for trapezoids. Write what you

discovered in the space below.

Page 16 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

16

Area of Composite Shapes

WARMUP:

What do we do if the shapes are MIXED? Mixed shapes are called “COMPOSITE” shapes. To find the

area you have to ___________________________________________________________________.

Total Area: _____________ square units (Hint: Get a ruler!)

Find the area of the irregular polygon below. Measurements have been provided

for you this time.

10 cm

5 cm

5 cm

4 cm

4 cm

8 cm 8 cm

2 cm

2 cm

Page 17 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

17

Practice…DRAW IT!

1. Find the area of a right triangle with a base length of three units, a height of four units, and a

hypotenuse of 5.

HINT: the hypotenuse is always the biggest side and isn’t part of the right angle.

2. Find the area of the trapezoid shown below using the formulas for rectangles and triangles.

3. A rectangle measures 3 inches by 4 inches. If the lengths of each side double, what is the effect

on the area?

12

7

3

Page 18 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

18

4. The lengths of the sides of a bulletin board are 4 feet by 3 feet. How many index cards

measuring 4 inches by 6 inches would be needed to cover the board?

5. The sixth grade class at Hernandez School is building a giant wooden H for their school. The

“H” will be 10 feet tall and 10 feet wide and the thickness of the block letter will be 2.5 feet.

1. How large will the H be if measured in square feet?

2. The truck that will be used to bring the wood from the lumberyard to the school can only

hold a piece of wood that is 60 inches by 60 inches. What pieces of wood (how many and

which dimensions) will need to be bought to complete the project?

6. A border that is 2 ft wide surrounds a rectangular flowerbed 3 ft by 4 ft. What is the area of the

border?

Page 19 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

19

Area of Composite Shapes HOMEWORK

Page 20 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

20

(Still Homework Day 3)

Page 21 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

21

Area Formulas and Parts of Equations/Expressions

Warm-up

Page 22 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

22

Shape within a Shape Game Cards

9)

Calculate the area of the shaded section in the picture

below:

15 cm

9 cm

10)

Mary’s father put a garden in their backyard that

had an area of 5 ft. by 9 ft. He put a sidewalk

around the garden that had an area of 7 ft. by 12 ft.

What is the area of the sidewalk around the

garden?

11)

Calculate the area of the shaded section in the picture

below: 12 yd

18 yd.

12)

The area of a local school is 3,844 sq. meters.

When they built the school they put a sidewalk

around the school. The dimensions of the

rectangle formed by the outer edge of the sidewalk

are 72 meters by 70 meters. What is the area of

the space between the school and sidewalk?

9cm

4 cm

The dimensions

of the inner

polygon are 3

yd. by 9 yd.

Page 23 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

23

13)

Calculate the area of the shaded section in the

picture below:

12 cm

11 cm

14)

Bob built his very own lemonade stand in front of

his house. His lemonade stand was 8 feet by 12

feet. He decided that he needed to make it look

nicer by planting flowers all the way around the

stand. The area of the rectangle formed around

the planted flowers was 130 sq. feet. How much

space was there between his lemonade stand and

the flowers?

15) Calculate the area of the shaded section in the picture

below:

15 ft.

12 cm

16)

Regulation NCAA basketball courts have

dimensions of 50 feet by 94 feet. There are chairs

around the entire court that make up an area of 56

feet by 100 feet. How much space is there just for

the chairs?

The dimensions

of the inner

polygon are 8cm

by 5 cm

The

dimensions

of the inner

polygon are

3ft by 6 ft

Page 24 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

24

ANSWERS for SHAPE WITHIN A SHAPE:

900 sq ft 34 sq ft 92 sq cm 189 sq yd

39 sq ft 162 sq. ft 1196 sq. m 5.495sq. ft

216.32 sq ft 1695.6 sq in 818.7 sq. ft 9.9416 sq. in

3.7994 sq. cm 130.44 sq. ft 16.5 sq. cm 99 sq cm

**Some answers above will not be used.

Page 25 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

25

Page 26 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

26

Page 27 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

27

Graph figure PQRS: P(-4, 3), Q(10, 3), R(10, -3),

S(-4, -3).

Determine the area and perimeter of the figure.

Give the coordinates of a figure that has a perimeter half

that of figure PQRS.

Give the coordinates of a triangle that has an area half that

of figure PQRS.

Graph rectangle :MNOP

)7,10(),7,4(),3,10(),3,4( PONM .

Determine the perimeter and area of the figure. Give the

coordinates for rectangle QRST that has the same area,

but a different perimeter.

Graph triangle :ABC ).3,8(),3,1(),9,4( CBA

Determine the area of the triangle. Give the coordinates

for a triangle DEF that has an area twice that of

triangle .ABC

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

-10 -8 -6 -4 -2 2 4 6 8 10

-10

-8

-6

-4

-2

2

4

6

8

10

Page 28 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

28

Page 29 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

29

Page 30 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

30

CCM6+ UNIT 8 STUDY GUIDE

PERIMETER AND AREA…Tell how to calculate the following. Write the formula if there is a formula!

1. Perimeter—

2. Area of a square—

3. Area of a rectangle—

4. Area of a parallelogram—

5. Area of a triangle—

What is different about the triangle formula? How will you remember this?

6. Area of mixed shapes—what do you do? What is tricky?

Page 31 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

31

WORD PROBLEMS

13) The perimeter of a rectangle is 12. Determine a possible length and width, then calculate a

possible area for that rectangle.

14) A rectangular photo is 5 inches long and 2 inches wide. Jimmy wants to enlarge the photo by

doubling its length and width. How many inches of wood will he need to make a frame for the

enlarged photo?

15) A figure is formed by a square and a triangle. Its total area is 32.5 m2. The area of the triangle is

7.5 m2. What is the length of each side of the square?

a) 5 meters b) 25 meters c) 15 meters d) 16.25 meters

16) A rectangle is formed by two congruent right triangles. The area of each triangle is 6 in2. If each

side of the rectangle is a whole number of inches, which of these could NOT be its perimeter?

a) 26 inches b) 24 inches c) 16 inches d) 14 inches

17) The volume of a cube is found with the formula V=s3 where the side length is represented by s. If

the side length is 11

2 inches, what is the volume of the cube?

18) The perimeter of a rectangle is 20 ft2. If the length is 5 ft, what is the AREA of the rectangle?

Page 32 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

32

For each problem:

Plot the ordered pairs in the coordinate plane given

Find the perimeter of the figure

Find the area of the figure

Find the distance between each point by using the absolute value

method.

19. G (-4, 5) H (5, 5)

I (-4, -5) J (5, -5)

Perimeter of GHIJ:__________

Area of GHIJ:_________

Page 33 CCM6 Unit 11 Angle Relationships, Area, Perimeter/Circumference

33

20. This figure is a four sided polygon. Before finding the area and

perimeter find the missing point.

R (-2, 2) S (4, 2) T ( , ) U ( -2, -3)

Perimeter of RSTU:__________

Area of RSTU:_________

What was the fourth vertex?

How did you find the length for

each side of the figure?

Find the area of the shaded region for each figure below.

21.

22.

Find the

Area and

Perimeter.