1 / 79

Chapter 10

Chapter 10 . Area. Area of Rectangles and Parallelograms. Area = bh Where b is the base and h is the height perpendicular to the base. A.k.a. altitude. Area of a triangle. A = ½ bh. Examples. Find the area of the following to the nearest tenth. 1) 2) 3) 4).

celine
Download Presentation

Chapter 10

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 10 Area

  2. Area of Rectangles and Parallelograms Area = bh Where b is the base and h is the height perpendicular to the base A.k.a. altitude

  3. Area of a triangle A = ½ bh

  4. Examples. Find the area of the following to the nearest tenth. 1) 2) 3) 4)

  5. Area of a trapezoid

  6. Example:

  7. Area of a Kite and Rhombus

  8. Examples: Find the area to the nearest tenth. 1) 2)

  9. Day 2 Area of Polygons

  10. Apothem is the perpendicular distance from the center to a side. (a)

  11. Radius: From the center of the polygon to a vertex of the polygon. Used to find the apothem

  12. Areas of Regular Polygons

  13. Areas of Regular Polygons Perimeter Apothem

  14. Theorem 10-6: Area of a Regular Polygon The area of a regular polygon is half the product of the apothem and the perimeter. A= ½ ap a = apothem p = perimeter

  15. Examples: Find the area to the nearest tenth. 1) 2)

  16. Example 1 Find the area of the octagon 9 in 7 in

  17. Examples • Find the area of each of the following: 11 yd 9 yd 12 cm 4 in 11 cm 9 in

  18. Using Special Right triangles • Use the properties of special right triangles to find the area of the hexagon. 10 in

  19. More Examples • Using properties of special right triangles, find the area of each hexagon. 6 3 m 12 yd

  20. Trigonometry and Area Find the area of the regular pentagon with 8cm sides. A = ½ (a)(40) 8 cm To find a: • Find the measure of < XCZ: • 360/5 = 72 C • Find the measure of < XCY: • 72/2 = 36 36 3. Use the triangle and trig to solve for a: a o = tan 36 = 4 a a a = 4 tan 36 a = 5.51 Use a to solve for area: A = ½ (5.51)(40) X 4 cm Z Y Area: 110.2 cm2

  21. Find the area of a regular octagon with a perimeter of 80 in. Give the area to the nearest tenth. To find the angle measure: 360/8 = 45 45/2 = 22.5 10 in o = tan 22.5 = 5 a a a = 5 tan 22.5 a = 12.07 a Use formula: A = ½ (12.07)(80) 5 in A = 482.8 in2

  22. Theorem 10.8: • The area of a triangle is one half the product of the lengths of two sides and the sine of the included angle. 3 Options:

  23. Finding the Area of a Triangle Area of Triangle ABC = ½ bh Area = ½ bc(sin A) Area = ½ (52)(24)(sin 76) Area = 605.46 in2 B a 24 in h 76 A C 52 in

  24. The surveyed lengths of two adjacent sides of a triangular plot of land are 412 ft and 386 ft. The angle between the sides is 71. Find the area of the plot. A = ½ bc(sin A) A = ½ (412)(386)(sin 71) 412 ft A = 75183.86 ft2 71 386 ft

  25. Two sides of a triangular building plot are 120 ft and 85ft long. They include an angle of 85. Find the area of the building plot to the nearest square foot. A = ½ bc(sin A) 85 85 ft A = ½ (120)(85)(sin 85) 120 ft A = 5081 ft2

  26. Warm Up • Find the area of a regular triangle with an apothem of 4”. • Find the area of a decagon with side lengths of 15 cm.

  27. Using Trigonometry

  28. Example

  29. Circles and Arcs Radius Diameter Center

  30. Central Angle Q R S An angle whose vertex is the center of the circle.

  31. Arcs • Semicircle: half of the circle • Minor Arc: smaller than a semicircle • Major Arc: Greater than a semicircle

  32. Example • Name three minor arcs, two semicircles, and three major arcs.

  33. Adjacent Arcs • Arcs of the same circle that have exactly one point in common • Arc Addition Postulate: The measure of the arc formed by two adjacent arcs is the sum of the measures of the two arcs

  34. Example • Find the measure of the following arcs 1. 2. 3. 4.

  35. Concentric Circles • Circles in the same plane with the same center Not Concentric Concentric

  36. Circumference In terms of pi Nearest tenth

  37. Arc Length • The length of the fraction of the circle’s circumference

  38. Area In terms of pi Nearest tenth

  39. Sector • A region bounded by an arc of the circle and two radii

  40. Area of a Sector • The product of the ratio of the sector and the area

  41. Examples: Find the area of the sector shaded.

  42. Segment • A part of a circle bounded by an arc and the segment joining its endpoints

  43. Area of the segment:

  44. Examples:

  45. Find the area of the shaded region:

  46. Geometric Probability

  47. Find the probability of getting a dart in the center of this triangular board:

  48. Find the probability of hitting one of the circles in the box with a dart:

  49. 12-1 Tangent Lines

  50. 12-1: Tangent Lines • Tangent to a circle: a line in the plane of the circle that intersects the circle in exactly one point. Point of Tangency

More Related