Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Trigonometric functions wikipedia , lookup
Tessellation wikipedia , lookup
Rational trigonometry wikipedia , lookup
Integer triangle wikipedia , lookup
Line (geometry) wikipedia , lookup
History of geometry wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Geometry Chapter 1 Lesson 1-6 Example 1 Identify Polygons Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular. a. b. Polygon JKLMN has five sides. It is a pentagon. If ML is extended, it passes through the interior of the pentagon. So, the pentagon is concave. Since it is concave pentagon JKLMN cannot be regular. Polygon RSTUVW has six sides, so it is a hexagon. No lines containing the sides of the hexagon pass through the interior. Therefore, the polygon is convex. Since all sides and all angles are congruent, hexagon RSTUVW is regular. Example 2 Find perimeter and area GARDENING A landscape designer is putting black plastic edging around a rectangular flower garden that has length 6.4 meters and width 5.7 meters. The edging is sold in 5-meter lengths. a. Find the perimeter of the garden and determine how much edging the designer should buy. P = 2 + 2w P = 2(6.4) + 2(5.7) = 6.4, w = 5.7 P = 12.8 + 11.4 or 24.2 The perimeter of the garden is 24.2 meters. The designer needs to buy 25 meters of edging, or 5 pieces. b. Suppose the designer needs to know the area of the garden in order to plan where to place each plant. Find the area of the garden. A = w A = (6.4) (5.7) = 6.4, w = 5.7 A = 36.48 The area of the garden is 36.48 square meters. 1 Geometry Chapter 1 Example 3 Test Example Bill wants to create a rectangular enclosure for his dog out of 84 feet of fencing. Which of the following shapes will have the greatest area? A a rectangle with length 26 and width 16 B a rectangle with length 30 and width 12 C a square with length and width of 21 D a rectangle with length 24 and width 18 Read the Test Item You are asked to compare the areas of four rectangles and choose the one with greatest area. Solve the Test Item Find the area of each rectangle. Rectangle A: A = w A = (26)(16) A = 416 Rectangle B: A = w A = (30)(12) A = 360 Rectangle C: A = w A = (21)(21) A = 441 Rectangle D: A = w A = (24)(18) A = 432 Since the square has greatest area, the answer is C Example 4 Perimeter and Area on the Coordinate Plane 2 Geometry Chapter 1 COORDINATE GEOMETRY Find the perimeter and area of triangle ABC if A(2, 7), B(5, 1) and C(-4, 1). Use the Distance Formula, d = (x2 - x1)2 + (y2 - y1)2, to find AB, BC and CA. AB = = (2 5) 2 (7 1) 2 (3) 2 (6) 2 = 45 ≈ 6.7 BC = = [5 (4)] 2 (1 1) 2 AC = (9) 2 (0) 2 = = 81 =9 The perimeter of triangle ABC is (4 2) 2 (1 7) 2 (6) 2 (6) 2 = 72 ≈ 8.5 45 + 72 + 9 or about 24.2 units. The height of the triangle is the perpendicular distance from A to BC . Counting the squares on the graph, the height is 6 units. The length of the base, BC , is 9 units. 1 A bh 2 1 A (9)(6) 2 A = 27 Area of a triangle Substitution Simplify. The area of triangle ABC is 27 square units. 3