Name: Period GL

UUNITNIT 12: A 12: AREAREA ANDAND P PERIMETERERIMETER

I can define, identify and illustrate the following terms: Perimeter AreaBaseHeight

Geometric probability DiameterRadius Circumference

Pi ( )Regular Polygon ApothemComposite FigureAltitude

Dates, assignments, and quizzes subject to change without advance notice.

Monday Tuesday Block Day Friday24

Parallelograms, Squares, and Rectangles

27Circles

Triangles and Trapezoids

28Regular Polygons

29/1Composite Figures

2Quiz

5Dimensional Changes

6Review

7/8Test Unit #12:Perimeter and

Area

9Geometric Probability

Activity

Friday, 2/24/12Area and Perimeter

I can find the area and perimeter of a polygon. I can solve problems using area, perimeter, and circumference

PRACTICE: p 38 (3-4, 10-11, 17-18, 21, 28, 44, 48) p 593 (1-3, 11-12,30-32, 34, 52-53)

Monday, 2/27/12Area and Perimeter

I can find the area and perimeter of a polygon. I can find the circumference of a circle. I can find the area of a circle.

PRACTICE: p38 (5-9, 12-16, 22-25) p593 (4-5, 14-16, 24-25, 35-36)

Tuesday, 2/28/12Regular Polygons

I can find the perimeter and area of a regular polygon.PRACTICE: Regular Polygons Worksheet

Block Day, 2/29/12- 3/1/12Composite Figures

I can find the area of composite figures.PRACTICE: Composite Figures Worksheet

1

Friday, 3/2/12Quiz

I can demonstrate my ability on all previously learned material.PRACTICE: Complete Any Unfinished Assignments

Monday, 3/5/12Dimensional Changes

I can describe an effect on perimeter or circumference when one or more dimensions are changed I can use scale factors to solve problems using dimensional changes.

PRACTICE: Dimensional Changes Worksheet

Tuesday, 3/6/12Review

I can assess my strengths and weaknesses on all previously learned material.

Block Day, 3/7-8/12

Test Unit #12: Area and Perimeter I can demonstrate my ability on all previously learned material.

Friday, 3/9/12Geometric Probability

I can calculate and use geometric probability to predict resultsPRACTICE: IN CLASS ACTIVITY

2

Area and Perimeter of Parallelograms, Rectangles and Squares

How do you find the perimeter of ANY figure? _____________________________________________

What is the formula for the area of a rectangle/square? ________________________

Consider the following diagram with given areas:

What can you conclude about the area of a parallelogram compared to the area of a rectangle?

What is the formula for the area of a parallelogram? ___________________________

Examples:

1. Find the area and perimeter of a rectangle with a width of 9.8 ft and a height of 2.7 ft.

2. Find the perimeter and area of a rectagle with length (s+3) and (s - 7).

3. Find the area and perimeter of a square with side lengths x.

4. Find the height of a parallelogram with base length 5 inches and area 12 inches.

5. Find the perimeter of a square with an area of 64 square centimeters.

3

44

10 44

10

Friday, 2/24/12 p 38 (3-4, 10-11, 17-18, 21, 28, 44, 48) p 593 (1-3, 11-12,30-32, 34)

4

Area and Perimeter of Circles, Triangles, and Trapezoids

PLEASE LEAVE ALL ANSWERS THAT HAVE Pi ( ) in them as Pi ( ). DO NOT ESTIMATE USING or 3.14.

Using your TAKS chart, write the formulas for the areas of the circle, triangle, and trapezoid.

Circle Triangle Trapezoid

What is the perimeter of a circle called? _______________________ Write the formula: ____________

Examples:

1. Find the circumference and area. Leave answers in terms of .

2. The area of a circle is 144 ft . Find the circumference.

3. Find the perimeter and area.

4. Find the perimeter and area. (use Pythagorean Theorem to help)

5. Find the perimeter of the isosceles trapezoid.

6. Find the height of a trapezoid if the bases have lengths of 6 and 17 and the area of the trapezoid is 46 square units.

5

13 in 13 in5 in

Monday, 2/27/12 p38 (5-9, 12-16, 22-25) p593 (4-5, 14-16, 24-25, 35-36)

6

7

Regular PolygonsEXAMPLES:Ex 1: Find the area of the regular polygon below.

For some figures you can use special right triangles to find the apothem of side length if it is not given.

Squares are made up of _____________ triangles.

Equilateral triangles and Hexagons are made up of ______________ triangles.

Label the sides of the triangle with the correct ratios.

Ex 2:

Ex 3:

Ex 3:

2 m

4 m

apothem

Tuesday, 2/28/12 Regular Polygon Worksheet8

5 in

13 in

45°

30°

60°

6 cm

r

(r + 6)

Find the area of each regular polygon.

1. 2. 3.

Area:______________ Area:______________ Area:______________

Area:______________ Area:______________ Area:______________

7. A regular heptagon has a perimeter of 35 feet, and an apothem of feet. What is the area?

8. A regular octagon has side lengths of 12 inches and an apothem of inches. What is the area?

9. The perimeter of a regular hexagon is 48 ft. What is the area of this polygon?

Name: Period: GH

9

8 cmxx + 3 y

y – 1

4. 5. 6.

Class Activity – Composite FiguresMaterials needed: four shapes, TAKS chart, blank paper, glue stick

I. Measuring Perimeter and Area

You and your partner will have four shapes. Each of you should take two of the shapes. Sketch your two shapes on this page. (Your sketches do not have to be perfectly to scale!)

For each shape:

Decide what lengths you need to know in order to calculate the perimeter. Measure these lengths to the nearest tenth of a centimeter and mark them on your diagram below. Use the ruler on your TAKS chart. DO NOT write the lengths on the shapes themselves.

Find the perimeter and write it underneath the diagram. Decide if you need any other measurements in order to find the area. Measure them and mark them

on your diagram. Find the area. Show all appropriate formulas and show your calculations.

Once you and your partner are finished measuring and calculating, switch shapes to verify each other’s calculations.

Diagrams and calculations:

10

II. Composite Figure

On a separate piece of paper, arrange your four shapes into one composite figure and glue them down. (Each shape must share at least one edge with another shape.)

Put your names on the paper. Sketch your composite figure below. (Does not have to be the real size.) Write in any relevant

lengths.

1. What is the perimeter of your composite figure?

2. What is the area of your composite figure? How did you figure it out? Write a few sentences explaining your process to someone having trouble with this concept.

11

Block Day, 2/29/12- 3/1/12 Composite Figures - Examples1 – 2: Find the area and outside perimeter for each figure. Assume all angles are right angles

1. 2.

3-9. Find the area of the shaded regions and the outside perimeter.

3. 4.

5. 6.

7. 8.

9. Mr. Ike wants to put brown tile in his living room except in the center where he wants ivory tile in a square shape. The diagram below shown the layout of the room. If each tile is a 6 inch square, how many brown tiles will he need? How many ivory tiles?

12

8 m

16 m6 m

3 m

8 m 9 m

5 in

7 in3 in

4 in

20 in

22 in

15 cm

6 cm6 cm

5 cm 6 cm3 cm

A = _____________

P = _____________

A = ________

P = _________

¼ x units

A = ________

P = _________

A = ________

P = _________

A = ________

P = _________

A = ________

P = _________

4 m3 m

A = ________

P = _________

A = ________

P = _________ 2 m2 m

3 m

10 ft

24 ft

42 in

Block Day, 2/29/12- 3/1/12 TAKS QUESTIONS OVER COMPOSITE FIGURES2006 Exit10. Four square pieces are cut from the corners of a square sheet of metal. As the size of the small squares increases, the remaining area decreases, as shown below.

If this pattern continues, what will be the difference between the first square’s shaded area and the fifth square’s shaded area?

A 4 square unitsB 24 square unitsC 49 square unitsD 96 square units

2003 Exit11. Find the equation that can be used to determine the total area of the composite figure shown below.

A A = lw + w2

B A = lw + w2

C A = w + 2l + w2

D A = w + 2l + w2

2006 Exit12. Look at the figure shown below. Which expression does not represent the area of the figure?

A bc − efB af + ad − deC de + af + adD af + cd

13

Monday, 3/5/12

Dimensional Changes

Use the figures below to answer questions #1 - 6.

1. Find the scale factor of the sides

2. Find the perimeter of ABCD 3. Find the perimeter of EFGH

4. Find the scale factor of the perimeters (EFGH / ABCD)

6. Find the area of ABCD 7. Find the area of EFGH

8. Find the scale factor of the areas (EFGH/ABCD)

9. How does the scale factor of the sides compare to the scale factor of the area?

10 Tony and Edwin each built a rectangular garden. Tony’s garden is twice as long and twice as wide as Edwin’s garden. If the area of Edwin’s garden is 600 square feet, what is the area of Tony’s garden?

11 The similarity ratio of two similar polygons is 3:5. The perimeter of the larger polygon is 150 centimeters. What is the perimeter of the smaller polygon?

2003 9th grade13. Describe the effect on the area of a circle when the radius is doubled.

F The area is reduced by .

G The area remains constant.H The area is doubled.J The area is increased four times.

2004 9th grade14. The similarity ratio of two similar polygons is 2:3. The perimeter of the larger polygon is 150 centimeters. What is the perimeter of the smaller polygon?

A 100 cmB 75 cmC 50 cmD 150 cm

14

4 cm

10 cm

6 cm

15 cmA B

CD

E F

GH