10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010 10.2 and 10.3 Areas of Kites, Rhombuses & Regular Polygons Objective: Find the areas of these shapes. Mar 28­2:49 PM 1 10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010 Warm­up Find the height a of each triangle. Then find the area. 30o 2. 1. a a o 18 25 10 Mar 28­5:20 PM 2 10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons Kites B A E D March 31, 2010 C What is the definition of a kite? How do you think we can find the area of a kite? What dimensions do we need to use your method? Mar 28­3:07 PM 3 10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010 Kites B A E What do you know about ΔABD and ΔCBD? C How would you find the area of ΔCBD in terms of the lengths AC and BD? D Mar 28­3:15 PM 4 10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010 Kites All we need to find the area of a kite is the length of both diagonals!!!! B A E C Akite = ½(d1 d2) D d1 = AC d2 = BD Mar 28­3:38 PM 5 10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010 Rhombuses C What is a rhombus? A D B E How do we find the area of a rhombus? Mar 28­3:44 PM 6 10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010 Rhombuses All we need to find the area of a rhombus is the length of both diagonals!!!! D C E A Arhombus = ½(d1 d2) B d1 = AC d2 = DB Mar 28­3:45 PM 7 10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010 Example #1: Find the area of the kite. Mar 28­4:07 PM 8 10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010 Example #2: Find the area of the rhombus. Mar 28­4:11 PM 9 10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010 Area of a Regular Polygon What does it mean for a polygon to be regular? How many sides does each polygon have? pentagon: octagon: hexagon: nonagon: decagon: Mar 28­4:13 PM 10 10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010 Area of a Regular Polygon What shape do we know how to find the area of, that we can split these regular polygons into? Mar 28­4:17 PM 11 10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010 Area of a Regular Polygon What is the measure of angle 1? What is the measure of angle 2? 1 2 What is the measure of angle 3? 3 Mar 28­4:33 PM 12 10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010 Area of a Regular Polygon How do we find the height a? How do we find the area of ΔABC? B 36o a What is the area of the pentagon? 54o A 6 C Mar 28­4:48 PM 13 10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010 Area of a Regular Polygon We found the area of ΔABC and then multiplied by the number of triangles in our shape. Areapolygon = Areatriangle x (# of sides) B Areapolygon = 12 a(base)(# of sides) 36o a 54o A 6 C Areapolygon = 12 ap where a = apothem p = perimeter so you know: AB is called the radius Mar 28­4:56 PM 14 10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010 Example #3: What are the measures of angles 1 and 2? 1 1 2 2 Mar 28­5:14 PM 15 10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010 Example #4: Find the area of the decagon. Mar 28­5:44 PM 16 10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010 Example #5: Find the area of the hexagon. Mar 28­5:46 PM 17 10.2 & 10.3 Areas of Kites, Rhombuses and Regular Polygons March 31, 2010 Homework Pg. 543 #11 ­ 16, 30 ­ 32 Pg. 548 # 4 ­ 18 even, 29 In many directions it says, "leave in simplest radical form". Don't worry about this, just round your answer to the nearest tenth. Mar 28­5:49 PM 18