7 ExamplesFind the area of RSTU.Find the area of the polygon RSTWUV.
8 ExampleOne diagonal of a kite is 1/3 as long as the other. The area of the kite is 0.24m2. What are the lengths of the diagonals?
9 11.3 Perimeter and Area of Similar Figures If two polygons are similar with the lengths of corresponding sides in the ratio a:b, then the ratio of their areas is a2:b2.
10 Example ABCD is similar to RSTU. Find the ratio of the perimeters. Find the ratio of the areas.
11 ExampleYou are painting 2 wall in an office complex that are similar in shape- both rectangles. One wall has a side length of 10ft. The corresponding side of the other wall is 14ft. You need 7 quarts to paint the larger wall. How many quart do you need for the smaller wall?
12 ExampleThe Pentagon in Washington DC is a regular pentagon with side lengths of 900ft. The area is 1,400,000ft2. The perimeter of a scale model of the building is 30yds. What is the area of the scale model?
13 11.4 Circumference and Arc length Circumference – the distance around the circle
14 Arc length- a portion of the circumference of a circle
17 11.5 Area of Circles and Sectors Area of a circle A = πr2Sector of a circle- region bounded by 2 radii of the circle and the intercepted arc.Sector APB = m AB πr o
18 ExampleFind the area of the sectors formed by <HJK.
19 ExampleFind the area between the large outer circle and the two smaller circles.
20 11.6 Areas of Regular Polygons The center of a polygon and the radius of a polygon are the center and radius of its circumscribed circle.Apothem of a polygon- distance from center to any side of a polygonCentral Angle of a regular polygon- the angle formed by 2 radii drawn to consecutive vertices of the polygon
23 ExamplesFor a regular octagon inscribed in circle C, find the following:m<RCY =m<RCZ =M<ZYC =
24 ExampleWhat is the area of a regular hexagon with a side length of 8 inches?
25 ExampleWhat is the area of a regular decagon inscribed in a circle with a radius of 8mm?
26 11.7 Using Geometric Probability Probability (of an event) - P(A)- a measure of the likelihood that an event will occur.Geometric probability is a ratio that involves a geometric measure like length or area.
27 ExampleFind the probability that a point chosen at random on AE is on CD.A B C D E
28 ExampleA dart game uses targets with concentric circles of radii 5,8, and 12 inches. What is the probability the dart will earn 20 points?