9.2. Polygons. Copyright 2005 Pearson Education, Inc.

Transcription

1 9.2 Polygons

2 Polygons Polygons are names according to their number of sides. Number of Sides Name Number of Sides Name 3 Triangle 8 Octagon 4 Quadrilateral 9 Nonagon 5 Pentagon 10 Decagon 6 Hexagon 12 Dodecagon 7 Heptagon 20 Icosagon Slide 9-2

3 Triangles The sum of the measures of the interior angles of an n-sided polygon is (n 2)180. Example: A certain brick paver is in the shape of a regular octagon. Determine the measure of an interior angle and the measure of one exterior angle. Slide 9-3

4 Triangles continued Determine the sum of the interior angles. S = ( n 2)180 o = (8 2)(180 ) o = 6(180 ) = 1080 o o The measure of one interior angle is o 1080 o = The exterior angle is supplementary to the interior angle, so = 45 Slide 9-4

5 Types of Triangles Slide 9-5

6 Similar Figures Two polygons are similar if their corresponding angles have the same measure and their corresponding sides are in proportion Slide 9-6

7 Example Catherine Johnson wants to measure the height of a lighthouse. Catherine is 5 feet tall and determines that when her shadow is 12 feet long, the shadow of the lighthouse is 75 feet long. How tall is the lighthouse? x Slide 9-7

8 Example continued ht. lighthouse lighthouse's shadow = ht. Catherine Catherine's shadow x 75 = x = 375 x = x Therefore, the lighthouse is feet tall Slide 9-8

9 Congruent Figures If corresponding sides of two similar figures are the same length, the figures are congruent. Corresponding angles of congruent figures have the same measure. Slide 9-9

10 Quadrilaterals Quadrilaterals are four-sided polygons, the sum of whose interior angles is 360. Quadrilaterals may be classified according to their characteristics. Slide 9-10

11 Classifications Trapezoid Parallelogram Two sides are parallel. Both pairs of opposite sides are parallel. Both pairs of opposite sides are equal in length. Slide 9-11

12 Classifications continued Rhombus Rectangle Both pairs of opposite sides are parallel. The four sides are equal in length. Both pairs of opposite sides are parallel. Both pairs of opposite sides are equal in length. The angles are right angles. Slide 9-12

13 Classifications continued Square Both pairs of opposite sides are parallel. The four sides are equal in length. The angles are right angles. Slide 9-13

14 9.3 Perimeter and Area

15 Formulas Figure Rectangle Square Parallelogram Triangle Trapezoid Perimeter P = 2l + 2w P = 4s P = 2b + 2w P = s 1 + s 2 + s 3 P = s 1 + s 2 + b 1 + b 2 A Area A = lw A = s 2 A = bh = 1 2 bh 1 A = h b1 + b2 2 ( ) Slide 9-15

16 Example Marcus Sanderson needs to put a new roof on his barn. One square of roofing covers 100 ft 2 and costs $32.00 per square. If one side of the barn roof measures 50 feet by 30 feet, determine a) the area of the entire roof. b) how many squares of roofing he needs. c) the cost of putting on the roof. Slide 9-16

17 Example continued a) The area of the roof is A = lw A = 30(50) A = 1500 ft (2 both sides of the roof) = 3000 ft 2 b) Determine the number of squares area of roof 3000 = = 30 area of one square 100 Slide 9-17

18 Example continued c) Determine the cost 30 squares $32 per square $960 It will cost a total of $960 to roof the barn. Slide 9-18

19 Pythagorean Theorem Slide 9-19

20 Example Tomas is bringing his boat into a dock that is 12 feet above the water level. If a 38 foot rope is attached to the dock on one side and to the boat on the other side, determine the horizontal distance from the dock to the boat. 12 ft 38 ft rope Slide 9-20

21 Example continued a + b = c b = b = b 2 = b b = The distance is approximately feet. Slide 9-21

22 Circles A circle is a set of points equidistant from a fixed point called the center. A radius, r, of a circle is a line segment from the center of the circle to any point on the circle. A diameter, d, of a circle is a line segment through the center of the circle with both end points on the circle. Slide 9-22

23 Example Terri is installing a new circular swimming pool in her backyard. The pool has a diameter of 27 feet. How much area will the pool take up in her yard? A A A = π r 2 = π(13.5) = The radius of the pool is 13.5 feet. The pool will take up about 573 square feet. Slide 9-23

24 Next Steps Study Examples 1,3,4 in 9.2 Study Examples 1-6 in 9.3 Do Online homework Do Online quiz once you ve studied both sections Slide 9-24