Assignment Guide: Chapter 10 Geometry (L3) (123) 10.1 Areas of Parallelograms and Triangles Page 619-621 #9-15 odd, 18-21, 24-30, 33, 35, 37, 41-43 (124) 10.2 Areas of Trapezoids, Rhombuses, and Kites Page 626-627 #11-25 odd, 33, 35, 37-39 (125) 10.3 Areas of Regular Polygons Page 632 #8-10, 21-29 (126) Review: 10.1 10.3 Worksheets (in assignment guide, page 9) Study for quiz (10.1 10.3) (127) Quiz: Sections 10.1 10.3 Page 634 #50-52 (128) 10.4 Perimeters and Areas of Similar Figures Page 638-640 #9-29 odd, 35-39 odd, 43 (129) 10.6 Circles and Arcs Page 654-656 #9-25, 31-35 odd, 37-42, 47, 53 (130) 10.7 Areas of Circles and Sectors Page 663-665 #7-31 odd, 38, 39, 43 (131) Review: 10.6 10.7 Worksheets (in assignment guide, page 17) Study for quiz (10.6 10.7) (132) Quiz: Sections 10.6 10.7 (133) 10.8 Geometric Probability Page 671-672 #8-16, 18-20, 21-24, 25-31 odd (134) Review: Chapter 10 Page 681 #1-21 Worksheets (in assignment guide, page 20 21) Study for Test (Chapter 10) (135) TEST: Chapter 10 Page 685 #1-12 This is a guide. Homework is subject to change. Check the chalkboard in class for updates and/or changes.
Geometry Notes Introduction to Chapter 10 Use your book to complete the table. Find the formula for Area (A) and what each variable ( s, b, h, d ) represents. Square A s Rectangle A h b Triangle A h b Parallelogram A h b Rhombus A d d 1 2 Trapezoid A b1 b 2 h Regular Polygon A Circle A a s p r 1
Geometry Notes, Section 10.1 Areas of Parallelograms and Triangles Area of a Parallelogram: A = bh Area of a Triangle: A = ½bh Try these: Find the area of each figure. 1. 2. 3. 4. Solve each problem by drawing a diagram, then using area formulas. 5. Find the area of a rectangle if its perimeter is 30 and its base is 8. 6. Find the area of a parallelogram with base 6 2 and height 10 2. 7. Find the area of an isosceles triangle with sides 30, 30, and 24. 8. The figure at the right consists of a parallelogram and a triangle. What is the area of the figure? 2
Geometry Practice, Section 10.1 Areas of Parallelograms and Triangles Solve each problem by drawing a diagram, then using area formulas. 11. Find the area of a parallelogram with base 6 cm and height 7 cm. 12. Find the area of an isosceles triangle with base 16 and perimeter 52. 13. Find the area of an equilateral triangle with sides 12 cm. 14. Find the area of a rhombus with perimeter 100 and one diagonal 14. 3
Geometry Notes, Section 10.2 Areas of Trapezoids, Rhombuses, and Kites Area of a Trapezoid: A = ½(b 1 +b 2 )h Area of a Rhombus: A = ½d 1 d 2 Area of a Kite: A = ½d 1 d 2 Try these: Find the area of each figure. 1. 2. 3. Solve each problem by drawing a diagram, then using area formulas. 4. The diagonals of a kite are in the ratio 3:2. The area of the kite is 27 cm 2. Find the length of both diagonals. 5. A trapezoid has two right angles, 16 in. and 20 in. bases, and 5 in. height. Sketch the trapezoid and find its perimeter and area. 6. In isosceles trapezoid EFGH, FG EH, FG = 10, GH = 12, and m E 60. Find the area of EFGH. 4
Geometry Practice, Section 10.2 Areas of Trapezoids, Rhombuses, and Kites Find the area of each trapezoid. Leave your answer in simplest radical form. 1. 2. 3. 4. Find the area of each rhombus. Leave your answer in simplest radical form. 5. 6. 7. 8. Find the area of each kite. Leave your answer in simplest radical form. 9. 10. 11. Find the area of each figure. Leave your answer in simplest radical form. 12. Find the area of a kite with diagonals 12 ft and 3 ft. 13. 14. 5
Geometry Notes, Section 10.3 Areas of Regular Polygons Area of a Regular Polygon: A = ½ap (a = apothem, p = perimeter) Try these: Find the area of each regular polygon shown. Round your answer to the nearest tenth. 1. 2. 3. Fill in the table with the radius (r), apothem (a), side (s), perimeter (p) and area (A) of each regular polygon. Equilateral Triangle r a s p A 1. 10 2. 6 3. 8 4. 15 5. 12 3 6
Geometry Practice, Section 10.3 Areas of Regular Polygons Fill in the table with the radius (r), apothem (a), side (s), perimeter (p) and area (A) of each regular polygon. Square r a s A 6. 144 7. 10 2 8. 7 9. 8 Regular Hexagon r a s p A 10. 4 11. 15 12. 6 13. 18 3 O is the center of a regular n-sided polygon with consecutive vertices A and B. 1. If AOB has the given measure, find the value of n. a) m AOB 45, n = b) m AOB 30, n = 2. Find the measure of a) AOB for the given value of n. a) n 10, m AOB b) n 15, m AOB 7
Find the apothem of each regular polygon. 3. Hexagon with radius 8 4. Square with side 10 5. Equilateral triangle with radius 4 3 Find the radius of each regular polygon. 6. Square with area 64 7. Triangle with apothem 12 3 Find the perimeter of each regular polygon. 8. Triangle with radius 4 3 9. Hexagon with radius 8 Find the area of each polygon described. 10. A square with perimeter 44 11. A square with apothem 4 12. A square with radius 6 13. A regular hexagon with radius 8 14. A regular hexagon with sides 12 15. An equilateral triangle with radius 6 16. An equilateral triangle with perimeter 36 18. A regular pentagon with perimeter 60 and apothem x 17. A regular 12-sided polygon with side s and apothem a 8
Geometry Review 10.1 10.3 Review: Areas of Polygons Find the area of each regular polygon. 13. 14. 9
Geometry Notes, Section 10.4 Perimeters and Areas of Similar Figures If the scale factor of two similar figures is a : b, then: - the ratio of their perimeters is a : b - the ratio of their areas is a 2 : b 2 Try these: The pair of figures is similar. Compare the larger figure to the smaller figure. Find the ratio of their perimeters and the ratio of their areas. 1. 2. 3. Scale factor: Ratio of perimeters: Ratio of areas: Scale factor: Ratio of perimeters: Ratio of areas: Scale factor: Ratio of perimeters: Ratio of areas: 4. The longer base of a right trapezoid is 12 ft. The longer base of a similar right trapezoid is 30 ft. The area of the smaller right trapezoid is 20 ft 2. What is the area of the larger right trapezoid? 5. A team is excavating an archeological site. The original plan was to excavate a rectangular area 35 ft long by 20 ft wide. Instead, the team decided to excavate a similar rectangle that is 50 ft wide. Find the length and the area of the new rectangle. 6. The area of a regular octagon is 45 ft 2. What is the area of a regular octagon with sides ⅓ the length of sides of the larger octagon? 10
Geometry Practice, Section 10.4 Perimeters and Areas of Similar Figures The figures in each pair are similar. Compare the first figure to the second. Give the ratio of the perimeters and the ratio of the areas. 1. 2. 3. The figures in each pair are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number. 4. The area of the smaller triangle is 12 in 2. 5. The area of the smaller parallelogram is 72 ft 2. 6. The area of the larger pentagon is 135 cm 2. 7. The area of the smaller rhombus is 60 m 2. The scale factor of two similar polygons is given. Find the ratio of their perimeters and the ratio of their areas. 15. 5 : 1 16. 2 : 7 17. 3 4 18. 10 7 19. 10 : 3 20. 5 9 21. A postcard costs $0.95. Leslie wants to buy a poster that is a similar shape with a scale factor for the poster to the postcard of 5 : 1. How much should she expect to pay for the poster? 11
Geometry Notes, Section 10.6 Circles and Arcs Circumference: the measure of the outside edge of a circle Arc: section of the circumference Types of Arcs: Minor arcs Semicircles Major arcs Degrees: Less than 180 Exactly 180 More than 180 Named by: Two endpoints Three points Three points Example: AB and CB ABC CAB Measure: = central = 180 = 360 minor arc Length: = (Measure/360 )(Circumference) Try these! Name the following in P. 1. the minor arcs 2. the major arcs 3. the semicircles Find the measure of each arc in A. 4. WX 5. XY 6. WY 7. WXZ 8. YZW 9. XZY 10. ZWX 11. WZ 12. WYX Find the length of each arc in R. Leave your answers in terms of. 13. SV 14. UV 15. SUT 16. UTV 17. UT 18. VT 19. How far does the tip of a minute hand on a clock travel in 20 minutes if the distance from the center to the tip is 9 cm? Leave your answer in terms of, then round it to the nearest tenth. 12
Geometry Practice, Section 10.6 Circles and Arcs 13
14
Geometry Notes, Section 10.7 Areas of Circles and Sectors Area of a Circle: A = r 2 Area of a Sector: A = (central angle/360 ) r 2 Try these! 15
Geometry Notes, Section 10.7 Areas of Circles and Sectors 16
Geometry Review 10.6 10.7 Review: Circles, Arcs, & Sectors 17
Geometry Notes, Section 10.8 Geometric Probability (review) Probability = # successes total (new) Geometric Probability = shaded area total area Geometry Practice, Section 10.8 18
Geometric Probability 19
Geometry Review Chapter 10 Review Find the area of each figure. 1. 2. 40 ^ 28 ^ 21 30 13 5 3. 8 in 14 in 5 in 24 in 4. 2 ft 5. 6. 2 3 cm 3 cm 4 m 7. 8. 9. Find the perimeter of a rectangle whose length is 14 cm, and whose area is 112 cm 2. 10. An octagon has an apothem of 21 inches, and a side length of 14 inches. Find its area. 11. A square has a diagonal of 16 mm. Find its area. 12. Find the area of a circle whose circumference is 8 yd. 20
13. A regular polygon has a perimeter of 6 ft, and an area of 36 ft 2. What is the length of its apothem? 14. Find the ratio of the areas of DEF to DEG. D E 12 F 15 G The scale factor of two similar figures is 3:8. 15. What is the ratio of their perimeters? 16. What is the ratio of their areas? For #15 16, use the diagram at right. 17. Find the length of arc AB. 18. Find the area of sector AOB. 19. Find the shaded area in the figure at right. What is the probability that a point chosen from each figure lies in the shaded area? 20. 11 7 21. 20 mm 21