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1-6 Two-Dimensional Figures

1-6 Two-Dimensional Figures. polygon – closed figure formed by a finite number of coplanar segments ( sides ) such that:. The sides that have a common endpoint are noncollinear . Each side intersects exactly two other sides at their endpoints ( vertices ).

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1-6 Two-Dimensional Figures

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  1. 1-6Two-Dimensional Figures polygon – closed figure formed by a finite number of coplanarsegments (sides) such that: • The sides that have a common endpoint are noncollinear. • Each sideintersects exactly two other sides at their endpoints (vertices)

  2. 1-6Two-Dimensional Figures Concave and Convex Polygons convex polygons concave polygons # of sides 3 4 5 6 7 8 polygon triangle quadrilateral pentagon hexagon heptagon octagon

  3. 1-6Two-Dimensional Figures equilateral polygon – has allsides congruent equiangular polygon – has allangles congruent regular polygon – has allangles and allsides congruent Name each polygon by its number of sides. Then, classify it as convex or concave and regular or irregular.   pentagon hexagon quadrilateral octagon concave convex convex concave irregular regular irregular irregular

  4. 1-6Two-Dimensional Figures perimeter – sum of the lengths of the sides of a polygon circumference – distancearound a circle area – number of squareunits needed to cover a surface Triangle Square Rectangle Circle C = 2r or C = d Perimeter Add up all of the sides A = r2 A = lw Area A = ½ bh A = s2

  5. 1-6Two-Dimensional Figures Find the perimeter (circumference) and area of each figure. d = 8 8.1 mm r = 8  2 = 4 C = 2r A = r2 P = 8 + 8.1 + 8.1 C = 2(3.14)(4) A = (3.14)(4)2 P = 24.2 mm C = 25.12 in A = (3.14)(16) A = ½ bh C = d A = 50.24 in2 A = ½ (8)(7) C = (3.14)(8) C = 25.12 in A = 28 mm2

  6. 1-7Three-Dimensional Figures polyhedron – solid with all flatsurfaces that enclose a single region in space face face – flat surface edge – line segment where faces intersect  vertex – corner; point where 3 or more edges intersect (plural: vertices) edge vertex Polyhedrons: pyramid prism

  7. 1-7Three-Dimensional Figures surface area – two-dimensional measurement of the surfaceof a solid volume – measure of amount of space enclosed by a solid figure Cylinder Rectangular Prism H h W L SA = 2rh + 2r2 SA = 2LW + 2WH + 2LH V = r2h V = LWH

  8. 1-7Three-Dimensional Figures Find the surface area and volume of each solid. rectangular prism V = LWH SA = 2LW + 2LH + 2WH V = (10)(5.2)(6) SA = 2(10)(5.2) + 2(10)(6) + 2(5.2)(6) V = 312 cm3 SA = 104 + 120 + 62.4 SA = 286.4 cm2

  9. 1-7Three-Dimensional Figures Find the surface area and volume of each solid. r = 12  2 = 6 12 ft cylinder V = r2h SA = 2rh + 2r2 V = 3.14(6)218 SA = 2(3.14)(6)(18) + 2(3.14)(62) V = 2034.72 ft3 SA = 678.24 + 226.08 SA = 904.32 ft2

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