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Perimeter and Area of Polygons

Perimeter and Area of Polygons. 3108.4.28  Derive and use the formulas for the area and perimeter of a regular polygon. . 3108.4.27   Use right triangle trigonometry to find the area and perimeter of quadrilaterals. Jim Smith JCHS.

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Perimeter and Area of Polygons

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  1. Perimeter and Area of Polygons 3108.4.28  Derive and use the formulas for the area and perimeter of a regular polygon.  3108.4.27  Use right triangle trigonometry to find the area and perimeter of quadrilaterals Jim Smith JCHS 3108.1.9    Expand analysis of units of measure to include area and volume.

  2. PERIMETER There are many formulas (or shortcuts) for finding the perimeter of polygons. The only one you need to remember is…. ADD ALL SIDES This will work for all polygons

  3. 8 5 5 3 3 4 4 8 8 7 P= 3+8+3+8=22 P= 4+5+5+4+7=25 P= 9+9+4=22 13 9 9 7 7 P= 13+7+4+7=31 4 4

  4. Area of Rectangles Think of filling the rectangle with boxes. All answers should be in square units. 4 4 Columns By 3 Rows 4X3= 12 3 This is the length times the width A= lw

  5. Rectangles 38 51 5 12 A=lw A=51x5 A=255 sq units A=lw A=38x12 A=456 sq units

  6. Area of Parallelograms h A=bh b The height must form a right angle with a base

  7. Parallelograms 7 15 6 10 A=bh A=10x7 A=70 sq. units A=bh A=15x6 A=90 sq. units

  8. Area of Triangles h h b b A=1/2 bh

  9. Triangles 7 21 A = 147 2 A = 73½ A = 73.5 sq units A = ½ bh A = ½ 7x21 A = ½ 147

  10. Equilateral or Isosceles Triangle Right Triangle 60° 10 10 8 5√3 60° 60° 6 5 5 10 A = ½ bh A = ½ 6 x 8 A = 24 Sq. Unit A = ½ bh A = ½ 10 x 5√3 A = 25√3 Sq. Unit

  11. Area of Trapezoids b1 h b2 A = ½ h( b1 + b2 )

  12. 8 Trapezoid 6 12 A = ½ h(b1 + b2) A = ½ (6)( 8+12 ) A = 3( 20 ) A = 60 sq units

  13. 45° 6 Trapezoid with 45° 8 6 45° 6 8 14 A = ½ h(b1 + b2) A = ½ 6( 8+14 ) A = ½ 6(22) A = 66 sq units

  14. 60° Isosceles Trapezoid 6 5√3 6 60° 5 5 16 5 A=1/2 h( b1+b2 ) A= ½ 5√3 ( 6+16 ) A= ½ 5√3 ( 22 ) A= 5√3 ( 11 ) A= 55√3 sq units

  15. Area of Rhombi and Kites d1 d2 d1 d2 ( d1 and d2 are the whole diagonals ) A = ½ d1 x d2

  16. Rhombus and Kite 10 4 8 6 7 X 3 6 8 4 A = ½ d1 x d2 A = ½ 12x16 A = 96 sq units A = ½ d1 x d2 A = ½ 8x10 A = 40 sq units

  17. Area of Regular Polygons s = side a = apothem r = radius r a s A=1/2 aP

  18. Regular Hexagon P = 6x6 P = 36 5 4 3²+x² = 5² 6 3 3 A = ½ aP A = ½ 4x36 A = 72 sq units

  19. The area of any figure is the sum of all the non-overlapping parts Triangle Trapezoid Rectangle

  20. + + + Add The Parts OR

  21. Complete the figure and subtract the part you don’t want ( bake the cake and eat the part you don’t want! )

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