11 1, 11-2 perimeter & area of polygons
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11 1, 11-2 perimeter & area of polygons

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11 1, 11-2 perimeter & area of polygons Presentation Transcript

  • 1. Perimeter and Area of Polygons Jim Smith JCHS 3108.1.9     Expand analysis of units of measure to include area and volume. 3108.4.27   Use right triangle trigonometry to find the area and perimeter of quadrilaterals   3108.4.28  Derive and use the formulas for the area and perimeter of a regular polygon. 
  • 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 8 8 3 3 9 9 4 13 7 5 4 7 4 5 4 7 P= 3+8+3+8=22 P= 4+5+5+4+7=25 P= 9+9+4=22 P= 13+7+4+7=31
  • 4. Area of Rectangles Think of filling the rectangle with boxes. All answers should be in square units. 4 3 4 Columns By 3 Rows 4X3= 12 This is the length times the width A= lw
  • 5. 5 51 38 12 A= lw A=51x5 A=255 sq units A= lw A=38x12 A=456 sq units Rectangles
  • 6. Area of Parallelograms h b A=bh The height must form a right angle with a base
  • 7. 7 10 15 6 A=bh A=10x7 A=70 sq. units A=bh A=15x6 A=90 sq. units Parallelograms
  • 8. Area of Triangles b b h h A=1/2 bh
  • 9. Triangles 21 7 A = ½ bh A = ½ 7x21 A = ½ 147 A = 147 2 A = 73½ A = 73.5 sq units
  • 10. Right Triangle Equilateral or Isosceles Triangle 6 8 A = ½ bh A = ½ 6 x 8 A = 24 Sq. Unit 10 10 10 60 ° 60 ° 60 ° 5 5 5 √ 3 A = ½ bh A = ½ 10 x 5 √ 3 A = 25 √ 3 Sq. Unit
  • 11. Area of Trapezoids b 1 b 2 h A = ½ h( b 1 + b 2 )
  • 12. 8 6 12 A = ½ h(b 1 + b 2 ) A = ½ (6)( 8+12 ) A = 3( 20 ) A = 60 sq units Trapezoid
  • 13. 45 ° 8 14 8 6 6 A = ½ h(b 1 + b 2 ) A = ½ 6( 8+14 ) A = ½ 6(22) A = 66 sq units Trapezoid with 45 ° 45 ° 6
  • 14. 60 ° 6 16 6 5 5 5 √ 3 5 A=1/2 h( b 1 +b 2 ) A= ½ 5 √ 3 ( 6+16 ) A= ½ 5 √ 3 ( 22 ) A= 5 √ 3 ( 11 ) A= 55 √ 3 sq units Isosceles Trapezoid 60 °
  • 15. Area of Rhombi and Kites d 1 d 2 A = ½ d 1 x d 2 d 2 d 1 ( d 1 and d 2 are the whole diagonals )
  • 16. Rhombus and Kite 10 8 X 6 8 6 A = ½ d 1 x d 2 A = ½ 12x16 A = 96 sq units 4 3 7 4 A = ½ d 1 x d 2 A = ½ 8x10 A = 40 sq units
  • 17. Area of Regular Polygons s r a s = side a = apothem r = radius A=1/2 aP
  • 18. 6 5 3 3 4 3 ²+x² = 5² A = ½ aP A = ½ 4x36 A = 72 sq units P = 6x6 P = 36 Regular Hexagon
  • 19. The area of any figure is the sum of all the non-overlapping parts Trapezoid Triangle 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! )