Geometry. 1.4 Perimeter and Area in the Coordinate Plane
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1 Geometry 1.4 Perimeter and Area in the Coordinate Plane
2
3 Essential Question How can I find the perimeter and area of a polygon in a coordinate plane?
4 What You Will Learn Classify polygons Find perimeters and areas of polygons in the coordinate plane.
5 Polygons A plane figure made of three or more segments (sides). Each side intersects exactly two other sides at their endpoints. Polygons are named by vertices in consecutive order, going CW or CCW.
6 Examples
7 These are NOT polygons. No Sides or Segments Sides don t intersect at endpoints. Figure not closed.
8 Naming Polygons The name tells you how many sides and how many vertices the polygon has. Learn the names: memorize! Be able to spell them.
9 Triangle 3 sides C We say Triangle ABC A B Vertex B
10 Quadrilateral 4 sides Q T Name: QRST We say Quadrilateral QRST R S
11 Pentagon 5 sides Name: JKLMN N J M K L
12 Hexagon 6 sides Name: FEDCBA C B D A E F
13 Heptagon 7 sides
14 Octagon 8 sides
15 Nonagon 9 sides
16 Decagon 10 sides
17 More than 10 sides: n-gon 14-gon has 14 sides. 200-gon has 200 sides. 36-gon has 36 sides.
18 Convex & Concave All polygons are either convex or concave. It s easy to determine which category falls in just by looking.
19 Convex No extended sides are in the interior of the polygon.
20 Concave Think: Caved In At least one extended side (or part of one) is in the interior of the polygon.
21 Example 1 Classify each polygon by the number of sides. Tell whether it is convex of concave. a. b. Quadrilateral, Concave Hexagon, Convex c. Heptagon, Convex d. Pentagon, Concave
22 Triangle Perimeter a h c P = a + b + c Area A 1 2 bh b
23 Square S Perimeter S P = 4s Area A = s 2
24 Rectangle Perimeter w P = 2 l + 2w l Area A = lw
25 Example 2 Each side of a square measures 2.5 m. Find its perimeter and its area. P = 4(2.5) = 10 m 2.5 m 2.5 m A = = 6.25 m 2 Area is a square measure.
26 Example 3 Find the perimeter and the area. 3 in 2 in 8 in 10 in P = = 21 in A = ½ (10)(2) = 10 in 2
27 Example 4 C(-2, 3) T(-2, -3) A(3,-3)
28 Example 5 D(1, 3) O(4,-3) G(-4, -3)
29 Example 6 You are building a shed in your backyard. The diagram shows the four vertices of the shed. Each unit in the coordinate plane represents 1 foot. Find the area of the floor of the shed.
30 Essential Question How can you find the perimeter and area of a polygon in a coordinate plane?
31 Assignment In the Student Math Jounals (the soft cover one) Do all the problems on page 20.
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