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Formulas geometry

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Formulas geometry

  1. 1. Formulas for Geometry Mr. Ryan Visit www.worldofteaching.com for more free powerpoints
  2. 2. Don’t Get Scared!!! <ul><li>Evil mathematicians have created formulas to save you time. But, they always change the letters of the formulas to scare you! </li></ul>
  3. 3. Perimeter <ul><li>Any shape’s “perimeter” is the outside of the shape…like a fence around a yard. </li></ul>
  4. 4. Perimeter <ul><li>To calculate the perimeter of any shape, just add up “each” line segment of the “fence”. </li></ul>
  5. 5. Perimeter <ul><li>Triangles have 3 sides…add up each sides length. </li></ul>8 8 8 8+8+8=24 The Perimeter is 24
  6. 6. Perimeter <ul><li>A square has 4 sides of a fence </li></ul>12 12 12 12 12+12+12+12=48
  7. 7. Perimeter <ul><li>Sometimes, problems may only give you two measurements for a square or rectangle. </li></ul><ul><li>No problem…use the formula for squares/rectangles (only!) </li></ul>
  8. 8. Remember <ul><li>Squares ALL sides are equal…so if they give you one side, you know ALL the sides </li></ul><ul><li>Length=the Largest side </li></ul><ul><li>If they “leave” numbers out, they are equal to their opposite side. If they give you the bottom of a square/rectangle type shape then the top is the same </li></ul>
  9. 9. The Same!! <ul><li>If the bottom is 15…the top is… </li></ul>15
  10. 10. Square/Rectangle Formula <ul><li>Perimeter=2(Length+Width) </li></ul><ul><li>P= 2(25+14) P=2(20+20) </li></ul><ul><li>P= 50+28 P=40+40 </li></ul><ul><li>P= 78 P=80 </li></ul>14 25 20
  11. 11. Other shapes <ul><li>Just add up EACH segment </li></ul>10 8 sides, each side 10 so 10+10+10+10+10+10+10+10=80
  12. 12. Odd shapes <ul><li>Count ALL sides </li></ul><ul><li>Remember if one side blank, it’s equal to its opposite </li></ul>25 15 5 25+25=50 (for Length) 15+5+15+5=40 (for Width) Perimeter=90
  13. 13. Area <ul><li>Area is the ENTIRE INSIDE of a shape </li></ul><ul><li>It is always measured in “squares” (sq. inch, sq ft) </li></ul>
  14. 14. AREA <ul><li>Square units means that “that” many squares fit inside that shape (if measured in feet…it’s feet…if meters…it’s meters. In this example the area is 4 square units…note 4 squares fit) </li></ul>2 units (ft, in, m) 2 3 4 1
  15. 15. Area of Squares/Rectangles <ul><li>Length x Width=Area </li></ul>2 Length(2) xWidth(2) = 4 square units
  16. 16. Parallelogram Area <ul><li>Same idea as squares & rectangles, but they change the words to Base (length:bottom of shape) and height (width) </li></ul>
  17. 17. Parallelogram Area <ul><li>Area=Base x Height </li></ul><ul><li>(Area=length x width) </li></ul>BASE (length) Height (width) 8 5 Base 8 x Height 5 = Area 40 The diagonal line is NOT the height!!!
  18. 18. REAL formula for area of squares <ul><li>Area= S^2 </li></ul><ul><li>Area= Side x Side (side squared) (just a different way of saying length x width) </li></ul>Side one Side two
  19. 19. Different Names/Same idea <ul><li>Length x Width = Area </li></ul><ul><li>Side x Side = Area </li></ul><ul><li>Base x Height = Area </li></ul>
  20. 20. Area of a Triangle <ul><li>½ Base x Height = Area </li></ul><ul><li>(It’s ½ because ½ of the “square” is missing) </li></ul>Base Height Height Base 8 5 ½ Base x Height = Area ½ (8) x 5 = Area 4 x 5 = 20
  21. 21. Area of a Circle <ul><li>Pi= 3.14 </li></ul><ul><li>Radius: from center (origin) of circle to ANY side </li></ul><ul><li>Area= pi x (Radius x Radius) </li></ul>
  22. 22. Circumference of a Circle <ul><li>Perimeter/Circumference = pi x diameter </li></ul><ul><li>Pi is always 3.14 </li></ul><ul><li>Circumference is a fancy name for perimeter </li></ul><ul><li>The diameter is a line from one side to the other side of a circle through its origin (It’s twice the radius) </li></ul>If the radius is 5, then the diameter is 10
  23. 23. Area of a circle <ul><li>Area = piR^2 </li></ul><ul><li>Pi = 3.14 and R=Radius </li></ul>Radius 5 Area=3.14 x (5 x 5) Perimeter = 3.14 x 10
  24. 24. You’re Done <ul><li>Squares, rectangles and parallelograms area are almost the same (LxW) </li></ul><ul><li>Triangles are ½ cause your missing ½ </li></ul><ul><li>Circles have fancy names, but just follow the formula </li></ul>
  25. 25.  <ul><li>For most tests you will have the formulas given to you. Just remember which one to use for which shape and you’ll do fine. </li></ul>

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