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11.4 Areas of Irregular Figures

11.4 Areas of Irregular Figures. Objective. Find areas of irregular figures. Irregular Figures. An irregular figure is a figure that cannot be classified into the specific shapes that we have already studied.

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11.4 Areas of Irregular Figures

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  1. 11.4 Areas of Irregular Figures

  2. Objective • Find areas of irregular figures

  3. Irregular Figures • An irregular figure is a figure that cannot be classified into the specific shapes that we have already studied. • To find the areas of irregular figures, separate the figure into nonoverlapping shapes of which we can find the area.

  4. Example 1: Find the area of the figure in square feet. Round to the nearest tenth if necessary. The figure can be separated into a rectangle with dimensions 16 feet by 32 feet, a triangle with a base of 32 feet and a height of 15 feet, and two semicircles with radii of 8 feet.

  5. Example 1: Area formulas Substitution Simplify. Use a calculator. Answer: The area of the irregular figure is 953.1 square feet to the nearest tenth.

  6. Your Turn: Find the area of the figure in square feet. Round to the nearest tenth if necessary. Answer:

  7. rose garden Example 2: A rectangular rose garden is centered in a border of lawn. Find the area of the lawn around the garden in square feet. The length of the entire lawn is 25 + 100 + 25 or 150 feet. The width of the entire lawn is 25 + 20 + 25 or 70 feet. The length of the rose garden is 100 feet and the width is 20 feet.

  8. area of irregular figure – area of rose garden Example 2: Area formulas Substitution Simplify. Simplify. Answer: The area of the lawn around the garden is 8500 square feet.

  9. Your Turn: INTERIOR DESIGNCara wants to wallpaper one wall of her family room. She has a fireplace in the center of the wall. Find the area of the wall around the fireplace. Answer:

  10. First, separate the figure into regions. Draw an auxiliary line perpendicular tofrom M (we will call this point S) and an auxiliary line from N to the x-axis (we will call this point K). Example 3: Find the area of polygon MNPQR. This divides the figure into triangle MRS, triangle NKM, trapezoid POKN and trapezoid PQSO.

  11. Example 3: Now, find the area of each of the figures. Find the difference between x-coordinates to find the lengths of the bases of the triangles and the lengths of the bases of the trapezoids. Find the difference between y-coordinates to find the heights of the triangles and trapezoids.

  12.  Area formulas Substitution Simplify. Example 3: Answer: The area of polygon MNPQR is 44.5 square units.

  13. Your Turn: Find the area of polygon ABCDE. Answer:

  14. Assignment • Pre-AP Geometry: Pg. 619 # 8 – 18, 20, 22, 25 - 27 • Geometry: Pg. 619 # 8 – 18, 20, 25 - 27

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