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Angles in pattern blocks Diagonals Joining two nonadjacent vertices of a polygon For which shapes will the diagonals always be perpendicular? Type of Quadrilateral Trapezoid Parallelogram Rhombus Rectangle Square Kite Are diagonals perpendicular? For which shapes will the diagonals always be perpendicular? Type of Quadrilateral Are diagonals perpendicular? Trapezoid maybe Parallelogram Rhombus Rectangle Square Kite For which shapes will the diagonals always be perpendicular? Type of Quadrilateral Are diagonals perpendicular? Trapezoid maybe Parallelogram maybe Rhombus Rectangle Square Kite For which shapes will the diagonals always be perpendicular? Type of Quadrilateral Are diagonals perpendicular? Trapezoid maybe Parallelogram maybe Rhombus yes Rectangle Square Kite For which shapes will the diagonals always be perpendicular? Type of Quadrilateral Are diagonals perpendicular? Trapezoid maybe Parallelogram maybe Rhombus yes Rectangle maybe Square Kite For which shapes will the diagonals always be perpendicular? Type of Quadrilateral Are diagonals perpendicular? Trapezoid maybe Parallelogram maybe Rhombus yes Rectangle maybe Square yes Kite For which shapes will the diagonals always be perpendicular? Type of Quadrilateral Are diagonals perpendicular? Trapezoid maybe Parallelogram maybe Rhombus yes Rectangle maybe Square yes Kite yes Sum of the angles of a polygon Use a minimum of five polygon pieces to create a 5-sided, 6-sided, 7 sided, 8-sided, 9-sided, 10sided, 11-sided, or 12-sided figure. Trace on triangle grid paper, cut out, mark and measure the total angles in the figure. 2 1 3 4 9 http://www.arcytech.org/java/patterns/patterns_j.shtml 8 2 1 5 7 3 6 4 7 5 6 Sum of the angles of a polygon Polygon # sides Triangle 3 Quadrilateral 4 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 Nonagon 9 Decagon 10 Undecagon 11 Dodecagon 12 Triskaidecagon 13 Nth N Total degrees What patterns do you see? Sum of the angles of a polygon Polygon # sides Total degrees Triangle 3 180 Quadrilateral 4 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 Nonagon 9 Decagon 10 Undecagon 11 Dodecagon 12 Triskaidecagon 13 nth n What patterns do you see? Sum of the angles of a polygon Polygon # sides Total degrees Triangle 3 180 Quadrilateral 4 360 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 Nonagon 9 Decagon 10 Undecagon 11 Dodecagon 12 Triskaidecagon 13 nth n What patterns do you see? Sum of the angles of a polygon Polygon # sides Total degrees Triangle 3 180 Quadrilateral 4 360 Pentagon 5 540 Hexagon 6 Heptagon 7 Octagon 8 Nonagon 9 Decagon 10 Undecagon 11 Dodecagon 12 Triskaidecagon 13 nth n What patterns do you see? Sum of the angles of a polygon Polygon # sides Total degrees Triangle 3 180 Quadrilateral 4 360 Pentagon 5 540 Hexagon 6 720 Heptagon 7 Octagon 8 Nonagon 9 Decagon 10 Undecagon 11 Dodecagon 12 Triskaidecagon 13 nth n What patterns do you see? Sum of the angles of a polygon Polygon # sides Total degrees Triangle 3 180 Quadrilateral 4 360 Pentagon 5 540 Hexagon 6 720 Heptagon 7 900 Octagon 8 Nonagon 9 Decagon 10 Undecagon 11 Dodecagon 12 Triskaidecagon 13 nth n What patterns do you see? Sum of the angles of a polygon Polygon # sides Total degrees Triangle 3 180 Quadrilateral 4 360 Pentagon 5 540 Hexagon 6 720 Heptagon 7 900 Octagon 8 1080 Nonagon 9 Decagon 10 Undecagon 11 Dodecagon 12 Triskaidecagon 13 nth n What patterns do you see? Sum of the angles of a polygon Polygon # sides Total degrees Triangle 3 180 Quadrilateral 4 360 Pentagon 5 540 Hexagon 6 720 Heptagon 7 900 Octagon 8 1080 Nonagon 9 1260 Decagon 10 Undecagon 11 Dodecagon 12 Triskaidecagon 13 nth n What patterns do you see? Sum of the angles of a polygon Polygon # sides Total degrees Triangle 3 180 Quadrilateral 4 360 Pentagon 5 540 Hexagon 6 720 Heptagon 7 900 Octagon 8 1080 Nonagon 9 1260 Decagon 10 1440 Undecagon 11 Dodecagon 12 Triskaidecagon 13 nth n What patterns do you see? Sum of the angles of a polygon Polygon # sides Total degrees Triangle 3 180 Quadrilateral 4 360 Pentagon 5 540 Hexagon 6 720 Heptagon 7 900 Octagon 8 1080 Nonagon 9 1260 Decagon 10 1440 Undecagon 11 1620 Dodecagon 12 Triskaidecagon 13 nth n What patterns do you see? Sum of the angles of a polygon Polygon # sides Total degrees Triangle 3 180 Quadrilateral 4 360 Pentagon 5 540 Hexagon 6 720 Heptagon 7 900 Octagon 8 1080 Nonagon 9 1260 Decagon 10 1440 Undecagon 11 1620 Dodecagon 12 1800 Triskaidecagon 13 nth n What patterns do you see? Sum of the angles of a polygon Polygon # sides Total degrees Triangle 3 180 Quadrilateral 4 360 Pentagon 5 540 Hexagon 6 720 Heptagon 7 900 Octagon 8 1080 Nonagon 9 1260 Decagon 10 1440 Undecagon 11 1620 Dodecagon 12 1800 Triskaidecagon 13 1980 nth n What patterns do you see? Sum of the angles of a polygon Polygon # sides Total degrees Triangle 3 180 Quadrilateral 4 360 Pentagon 5 540 Hexagon 6 720 Heptagon 7 900 Octagon 8 1080 Nonagon 9 1260 Decagon 10 1440 Undecagon 11 1620 Dodecagon 12 1800 Triskaidecagon 13 1980 nth n ? What patterns do you see? Sum of the angles of a polygon Polygon # sides Total degrees Triangle 3 180 Quadrilateral 4 360 Pentagon 5 540 Hexagon 6 720 Heptagon 7 900 Octagon 8 1080 Nonagon 9 1260 Decagon 10 1440 Undecagon 11 1620 Dodecagon 12 1800 Triskaidecagon 13 1980 nth n 180(n-2) What patterns do you see? Total degree of angles in polygon Area Formulas: Triangle Ø http://illuminations.nctm.org/LessonDetail.aspx?ID=L577 Area Formulas: Triangle 1. Using a ruler, draw a diagonal (from one corner to the opposite corner) on shapes A, B, and C. 2. Along the top edge of shape D, mark a point that is not a vertex. Using a ruler, draw a line from each bottom corner to the point you marked. (Three triangles should be formed.) 3. Cut out the shapes. Then, divide A, B, and C into two parts by cutting along the diagonal, and divide D into three parts by cutting along the lines you drew. 4. How do the areas of the resulting shapes compare to the area of the original shape? Area Formulas: Triangle Area Formulas: Triangle Area Formulas: Trapezoids Ø http://illuminations.nctm.org/LessonDetail.aspx?ID=L580 Area Formulas: Trapezoids Do you have suggestions for finding area? What other shapes could you use to help you? Are there any other shapes for which you already know how to find the area? Area Formulas: Trapezoids 18cm 13 cm 15 cm 11cm 24 cm Connect Math Shapes Set http://phcatalog.pearson.com/component.cfm? site_id=6&discipline_id=806&subarea_id=1316&program_id=23245&pr oduct_id=3502 CMP Cuisenaire® Connected Math Shapes Set (1 set of 206) ISBN-10: 157232368X ISBN-13: 9781572323681 Price: $29.35 Area Formulas: Trapezoids A = ½h(b1 + b2) When triangles are removed from each corner and rotated, a rectangle will be formed. It s important for kids to see that the midline is equal to the average of the bases. This is the basis for the proof—the midline is equal to the base of the newly formed rectangle, and the midline can be expressed as ½ (b1 + b2), so the proof falls immediately into place. To be sure that students see this relationship, ask, "How is the midline related to the two bases?" Students might suggest that the length of the midline is "exactly between" the lengths of the two bases; more precisely, some students may indicate that it is equal to the average of the two bases, giving the necessary expression. Remind students that the area of a rectangle is base × height; for the rectangle formed from the original trapezoid, the base is ½(b1 + b2) and the height is h, so the area of the rectangle (and, consequently, of the trapezoid) is A = ½h(b1 + b2). This is the traditional formula for finding the area of the trapezoid. Area Formulas: Trapezoids 18cm 13 cm 15 cm 11cm 24 cm Area Formulas: Trapezoids Websites: http://argyll.epsb.ca/jreed/math9/strand3/ trapezoid_area_per.htm dDwxNTM Parallelograms dDwxNTM Ø A = Length x width Ø http://illuminations.nctm.org/LessonDetail.aspx?ID=L578 Area of Parallelogram Can you estimate the area of Tennessee? Area of irregular figure? Find the area of the irregular figure. Area of irregular figure? Area of irregular figure? Circles Area = πr2 Circumference = 2 πr or Circumference = π d Circles Otis is drawing a circle with a 4 inch radius. He wants to double the radius. How will this affect the area of the circle? Circles Su is selling 12 inch diameter pumpkin pies for $6.50. How should she adjust her price (if she wants to be fair) when she reduces her pies to a 10 inch diameter? Circles Javier s bicycle tire has a 12 inch radius. How far will he travel. . . . . . in one rotation of the tire? . . . in 10 rotations of the tire?
