Name:__________________________________________________ Date: _______________

Geometry 2011-2012

Area of Polygons

And Circles

Name:______________________________

Teacher:____________________________

Pd: _______

Table of Contents

DAY 1: SWBAT: Calculate the area and perimeter of Parallelograms and Triangles

Pgs: 1 - 5

HW: Pgs: 6-7

DAY 2: SWBAT: Calculate the area of Trapezoids and Rhombi Pgs: 8-12

HW: Pgs: 13 - 14

DAY 3: SWBAT: Calculate the area and Circumference of Circles

Pgs: 15 - 20

HW: Pgs: 21 - 23

DAY 4: SWBAT: Calculate area of Regular Polygons

Pgs: 24-29

HW: Pgs: 30 - 31

DAY 5: SWBAT: Calculate the areas of similar figures by using scale factors

Pgs: 32 - 36

HW: Pg 37

Extra Practice

Pgs: 38-42

1

Day 1- SWBAT: Calculate the area of Parallelograms and Triangles

Recall the formulas for calculating area of Parallelograms and Triangles…

Area (rectangle)

LWA

Area (square)

s A 2

Area (parallelogram)

bhA

Area (triangle)

2

bhAorbh

2

1A

Triangle

2

Section 1: Calculate the area and Perimeter of each.

Example Perimeter Area 1.

2.

3.

4.

5.

3

Example Perimeter Area

6.

7.

8.

9.

10.

4

Section 2: More Challenging Problems

11.

12.

13.

Section 3: Finding the missing dimension, given the area.

14. 15. 16.

5

Find the missing height.

17. 18.

Challenge

SUMMARY

Exit Ticket

6

Day 1: Homework

Calculate the area and perimeter or each. 1.

2.

3.

4.

5.

6.

7.

8.

7

Calculate the area and perimeter of problems 9-12.

9.

10.

11.

12.

13. Find the height of a parallelogram with an

area of 153 in2 and a base of 9 in.

14. Calculate the height of a triangle with an

area of 165 cm2 and a base of 41 cm.

15. Calculate the diagonal of a square with an

area of 64 cm2. Leave your answer in simplest

radical form.

16. Calculate the length of a rectangle with a

width of 14 cm and an area of 70 cm2.

8

Day 2- SWBAT: Calculate the area of Trapezoids and Kites

Warm - UP

1.

2.

9

Section 1: Level A - Calculate the area of each trapezoid.

1.

2.

3.

4.

Section 2: Level B - Calculate the area of each trapezoid.

5.

10

6.

7.

11

Section 3: Level A - Calculate the area of each rhombus.

8.

9.

10.

**11.

Section 4: Given the area calculate the missing dimension

12. A trapezoid has base lengths of 6 and 15 centimeters with an area of 136.5 square cm. What is the height

of the trapezoid? 13. One diagonal of a rhombus is twice as long as the other diagonal. If the area of the rhombus is 400 square meters, what are the lengths of the diagonals?

12

Challenge

SUMMARY

Exit Ticket

13

Day 2 – Homework

Calculate the area of each.

1.

2.

3.

4.

5.

6.

14

7.

8. A trapezoid has a height of 24 meters, a base of 4

meters, and an area of 264 square meters. What is the length of the other base?

9.

10.

11. A rhombus has sides of length 10 m. and one

diagonal of length 16 m. Find its area.

12. The longer diagonal of a rhombus is 3 times as

long as the shorter diagonal. Find the length of the shorter diagonal if the area is 24 in2.

15

Day 3 – Area and Circumference of Circles

Warm - Up

1.

2.

16

Section 1: Calculate the Circumference and Area of each Circle. Leave your answers in terms of .

Example Circumference Area

1.

2.

3.

4.

17

Section 2: Calculate the circumference or area given the circumference or area.

5. The circumference of a circle is 26 . Calculate the diameter, radius, and area of the

circle.

6. The circumference of a circle is 20 . Calculate the diameter, radius, and area of the

circle.

7. The area of a circle is 64 . Calculate the diameter, radius, and circumference of the

circle.

8. The area of a circle is 169 . Calculate the diameter, radius, and circumference of

the circle.

18

Section 3: Areas of Sectors

9.

10. Lkj

19

Shaded Area

11. 11.

12. 12.

20

Challenge

Summary

Exit Ticket

21

Day 3 – Homework

Calculate the Circumference and Area of each Circle. Leave your answers in terms of .

Example Circumference Area

1.

2.

3.

4.

5.

6.

22

7. The circumference of a circle is 50 . Calculate the diameter, radius, and area of the

circle.

8. The circumference of a circle is 40 . Calculate the diameter, radius, and area of the

circle.

9. The area of a circle is 225 . Calculate the diameter, radius, and circumference of the

circle.

10. The area of a circle is 16 . Calculate the diameter, radius, and circumference of the

circle.

23

11. Calculate the area of the shaded region.

12. Calculate the area of the shaded region.

13. Calculate the area of the sector. Round your answers to the nearest hundredth.

14. Calculate the area of the sector. Round your answers to the nearest hundredth.

24

Day 4 – Area of Regular Polygons

Warm – Up

The Area of an Equilateral Triangle

Formula =

Example A

25

The Area of a Regular Polygon

Derivation of the formula to calculate the Area for any Regular Polygon

26

Steps to Calculate the area of a Regular Polygon.

Section 1: Calculating Area given the apothem

Example 1:

Example 2:

27

You Try It!

Radius = 10, apothem = 9.4, side = 3

Regular Hendecagon. Radius = 5.7, and apothem = 5.5

28

Section 2: Calculating the area with the apothem not given.

4

12

a

29

Challenge

SUMMARY

Exit Ticket

b. Equilateral Triangle

A 110.9 in2

30

Day 4 – Homework/ Area of Regular Polgyons

Calculate the area of each equilateral triangle.

1.

2.

3. Find the area of an equilateral triangle that has a perimeter of 48 inches.

4. Find the area of an equilateral triangle that has a perimeter of 60 inches.

5.

6.

7. 8.

31

Find the length of each side first, and then calculate the area of each polygon to the nearest hundredth.

9. 10.

Find the length of each apothem first, and then calculate the area in simplest radical form.

11. 12.

33

32

Day 5 – Areas and Similar Polygons

Warm – Up

33

Example 1:

You Try It!

Example 2:

The areas of two similar are 50cm2 and 18 cm

2. What is the similarity ratio? What is the ratio

of their perimeters?

You Try It!

The areas of two similar are 338 cm2 and 98 cm

2. What is the similarity ratio? What is the ratio

of their perimeters?

34

Example 3:

You Try It!

a.

b.

35

Example 4: Using Area of Similar Figures to find Side Lengths

You Try It!

a. b.

36

Challenge

The two polygons are similar. Find the value of x.

SUMMARY

Exit Ticket

37

Day 5 - Homework

38

Day 6 – Review

Area of Equilateral Triangle =

C = or

39

Using 30-60-90 and 45-45-90 Concepts

Calculate area and Perimeter.

15a. 15b.

40

20a.

41

42

Answer Key

15. 132 sq. ft

15a. P = 38 units; A = ( * 13) ≈67.5 sq units

15b. P = 68 units; A = ( * 24) ≈169.7 sq units

16. A = 84 square units

17. A = 96 square cm

18. A = 168 square ft

19. A = 336 square cm

20. A = 6 square ft

20a. A = 60 + 72

21. A = 1.5 square meters

22. A = 175.8 square inches

23. A = 59 square in

24. 50.27 in2, 33.51 in

2, 117.29 in

2

25. A = 166.3 ft2

26. A = 101.8 cm2

27. A = 65 m2

28.