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11.4 Areas of Irregular Figures

11.4 Areas of Irregular Figures. By Paige Ketch and Brandi Lazarus. Objectives. Find areas of irregular figures. Find areas of irregular figures on a coordinate plane. Irregular Figures. An Irregular Figure is a figure that cannot be classified as a single polygon.

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11.4 Areas of Irregular Figures

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  1. 11.4 Areas of Irregular Figures By Paige Ketch and Brandi Lazarus

  2. Objectives • Find areas of irregular figures. • Find areas of irregular figures on a coordinate plane.

  3. Irregular Figures • An Irregular Figure is a figure that cannot be classified as a single polygon. • Segments EB and FB separate figure ABCD into ABE and BFC and rectangle EBFD. A B E A D C F

  4. Area of Irregular Figures • Postulate 11.2- The area of a region is the sum of all of its nonoverlapping parts. • To find the area of the entire figure, separate it into known figures that do not overlap then find the areas of the individual shapes. Then add.

  5. Example 1 Find the area of the shape. 27 8 13

  6. Separate into individual shapes. • Find areas of regular shapes then add. • Area of irregular shape = area of triangle + area of rectangle + area of semicircle. 27 8 13

  7. A = ½bh + bh + ½ πr ² Area formulas A = ½ (27-13)(8) + (8)(13) + ½ π 4² Substitution A = ½ (112) + 104 + ½ (50.3) simplify A = 56 + 104 + 25.2 simplify A = 185.2 units ² solve

  8. Example 2 Find the area of the irregular shape by finding the area of the rectangle and subtracting the area of the triangle. 18 11 6

  9. A = bh – ½ bh Area formulas A = (6 • 18) – ½(6 • 7) Substitution A= 108 – 21 Simplify A = 87 units ² Solve

  10. Your turn 28 24

  11. The semicircle cut out of the shape and the semicircle attached to the shape are congruent, therefore you only have to find the area of the rectangle. A = bh Area formula A = 24 • 28 Substitution A = 672 units² Solve

  12. Example 3 Find the area of the shape • Since the four triangles are congruent, use the area formula for a triangle and multiply by four.

  13. A = 4(½ bh) + bh Area formulas A = 4 [½ (4)(5)] + (4)(4) Substitution A = 4(10) + 16 Simplify A = 40 + 16 Simplify A = 56 units² Solve

  14. Your Turn Find the area of the shape

  15. Separate into known figures

  16. ¹ ² A = ½ bh + ½ h (b + b ) Area formulas A = ½ (3 • 5) + ½ (5)(3 + 8) Substitution A = ½ (15) + ½ (55) Simplify A = 7.5 + 27.5 Simplify A = 35 units² Solve

  17. Assignment Pre-AP Geometry: P. 619 #3-15 all and #16-20 even

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