11 1, 11-2 perimeter & area of polygons

1,967 views

Published on

Published in: Education
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
1,967
On SlideShare
0
From Embeds
0
Number of Embeds
11
Actions
Shares
0
Downloads
116
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

11 1, 11-2 perimeter & area of polygons

  1. 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. 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. 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. 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. 5 51 38 12 A= lw A=51x5 A=255 sq units A= lw A=38x12 A=456 sq units Rectangles
  6. 6. Area of Parallelograms h b A=bh The height must form a right angle with a base
  7. 7. 7 10 15 6 A=bh A=10x7 A=70 sq. units A=bh A=15x6 A=90 sq. units Parallelograms
  8. 8. Area of Triangles b b h h A=1/2 bh
  9. 9. Triangles 21 7 A = ½ bh A = ½ 7x21 A = ½ 147 A = 147 2 A = 73½ A = 73.5 sq units
  10. 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. 11. Area of Trapezoids b 1 b 2 h A = ½ h( b 1 + b 2 )
  12. 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. 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. 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. 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. 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. 17. Area of Regular Polygons s r a s = side a = apothem r = radius A=1/2 aP
  18. 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. 19. The area of any figure is the sum of all the non-overlapping parts Trapezoid Triangle Rectangle
  20. 20. + + + Add The Parts OR
  21. 21. Complete the figure and subtract the part you don’t want ( bake the cake and eat the part you don’t want! )

×