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
Day 1- SWBAT: Calculate the area of Parallelograms and Triangles Recall the formulas for calculating area of Parallelograms and Triangles Area (rectangle) A LW Area (square) A s 2 Area (parallelogram) A bh Triangle Area (triangle) 1 A bh or A 2 bh 2 1
Section 1: Calculate the area and Perimeter of each. Example Perimeter Area 1. 2. 3. 4. 5. 2
Example Perimeter Area 6. 7. 8. 9. 10. 3
Section 2: More Challenging Problems 11. 12. 13. Section 3: Finding the missing dimension, given the area. 14. 15. 16. 4
Find the missing height. 17. 18. Challenge SUMMARY Exit Ticket 5
Day 1: Homework Calculate the area and perimeter or each. 1. 2. 3. 4. 5. 6. 7. 8. 6
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 in 2 and a base of 9 in. 14. Calculate the height of a triangle with an area of 165 cm 2 and a base of 41 cm. 15. Calculate the diagonal of a square with an area of 64 cm 2. 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 cm 2. 7
Day 2- SWBAT: Calculate the area of Trapezoids and Kites Warm - UP 1. 2. 8
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. 9
6. 7. 10
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? 11
Challenge SUMMARY Exit Ticket 12
Day 2 Homework Calculate the area of each. 1. 2. 3. 4. 5. 6. 13
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 in 2. 14
Day 3 Area and Circumference of Circles Warm - Up 1. 2. 15
Section 1: Calculate the Circumference and Area of each Circle. Leave your answers in terms of. Example Circumference Area 1. 2. 3. 4. 16
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. 17
Section 3: Areas of Sectors 9. 10. Lkj 18
Shaded Area 11. 11. 12. 12. 19
Challenge Summary Exit Ticket 20
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. 21
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. 22
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. 23
Day 4 Area of Regular Polygons Warm Up The Area of an Equilateral Triangle Formula = Example A 24
The Area of a Regular Polygon Derivation of the formula to calculate the Area for any Regular Polygon 25
Steps to Calculate the area of a Regular Polygon. Section 1: Calculating Area given the apothem Example 1: Example 2: 26
You Try It! Radius = 10, apothem = 9.4, side = 3 Regular Hendecagon. Radius = 5.7, and apothem = 5.5 27
Section 2: Calculating the area with the apothem not given. 4 12 a 28
Challenge SUMMARY b. Equilateral Triangle A 110.9 in 2 Exit Ticket 29
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. 30
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 31
Day 5 Areas and Similar Polygons Warm Up 32
Example 1: You Try It! Example 2: The areas of two similar are 50cm 2 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 cm 2 and 98 cm 2. What is the similarity ratio? What is the ratio of their perimeters? 33
Example 3: You Try It! a. b. 34
Example 4: Using Area of Similar Figures to find Side Lengths You Try It! a. b. 35
Challenge The two polygons are similar. Find the value of x. SUMMARY Exit Ticket 36
Day 5 - Homework 37
Day 6 Review Area of Equilateral Triangle = C = or 38
Using 30-60-90 and 45-45-90 Concepts Calculate area and Perimeter. 15a. 15b. 39
20a. 40
41
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 in 2, 33.51 in 2, 117.29 in 2 25. A = 166.3 ft 2 26. A = 101.8 cm 2 27. A = 65 m 2 28. 42