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Area of Regular Polygons

Area of Regular Polygons. Break the figure down into triangles. 4. 5. 3. 6. 2. 1. Notice there are 6 triangles and 6 sides. 4. 5. 3. 6. 2. 1. Let’s look at 1 of the triangles closer. The area of a triangle is:. h. b. Area = ½bh.

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Area of Regular Polygons

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  1. Area of Regular Polygons

  2. Break the figure down into triangles

  3. 4 5 3 6 2 1 Notice there are 6 triangles and 6 sides

  4. 4 5 3 6 2 1 Let’s look at 1 of the triangles closer

  5. The area of a triangle is: h b Area = ½bh

  6. When the triangle is part of a polygon, the height is called the Apothem apothem h b

  7. There are 6 triangles, so we have to multiply our area by 6! apothem base Of course, using the equation you’ll only find the area for one of the triangles.

  8. Another way to look at it is that we have 6 bases and one apothem apothem base Remember, 6 times the base is the perimeter of the object!

  9. Therefore we can use the formula: apothem base 1 __ ap Area = 2 Perimeter

  10. Ex: Find the area of the hexagon 8 5 1 __ ap Area = 2 First we must find the perimeter: p = 5(6) = 30

  11. Find the area of the hexagon 8 5 1 1 __ __ ap 8(30) Area = Area = 2 2 Plug everything in p = 5(6) = 30

  12. Find the area of the hexagon 8 5 1 __ 8(30) Area = 2 Solve = 120

  13. Practice 1 • Find the area of the following regular polygons: • Octagon with base of 4 and apothem 7 • Hexagon with base of 8 and apothem 3 • The figure below 12 10

  14. But what if we’re not given the apothem?? 1 __ ap Area = 2

  15. Ex: Find the area of the polygon 10 1 __ ap Area = We need the perimeter and apothem 2

  16. 4 5 3 6 2 1 Let’s look at 1 of the triangles closer again

  17. a 10 Inside we have two right triangles

  18. We can find the angle at the top and use it to find the apothem a 10

  19. There’s 3600 around the center of the figure Since there’s 6 sides we can find the angle at the top of each triangle by: 360 = 60 6

  20. 600 The top angle is 60 and the apothem cuts it in half a 300

  21. 300 Half the triangle means half the base a 5 This is now a 30-60-90 right triangle! The apothem is:

  22. Ex: Find the area of the polygon 10 1 __ ap Area = 2 We need the perimeter and apothem

  23. Ex: Find the area of the polygon 10 1 __ ap Area = 2

  24. 6 But what if it’s not a special right triangle?? 1 __ ap Area = 2 360 = 72 5

  25. 360 Break it down to the small triangle a 3 The angle gets cut in half The base is cut in half

  26. 360 Use the trig function to find apothem hyp a adj 3 opp

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