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Areas of Irregular Figures

Learn how to find areas of irregular figures by separating them into recognizable shapes like triangles and rectangles. Practice examples and steps included.

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Areas of Irregular Figures

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  1. Areas of Irregular Figures • Find areas of irregular figures. • Find areas of irregular figures on the coordinate plane. The wind surfer’s sail can be separated into figures that can be identified, such as trapezoids and a triangle.

  2. IRREGULAR FIGURES An irregular figurecannot be classified as a specific shape that we have studied. To find areas of irregular figures, separate the figure into shapes of which we can find the area. A D C B

  3. IRREGULAR FIGURES An irregular figure cannot be classified as a specific shape that we have studied. To find areas of irregular figures, separate the figure into shapes of which we can find the area. A Auxiliary lines are drawn in quadrilateral ABCD. The figure is separated into two triangles and a rectangle. D E C B F

  4. Postulate The area of a region is the sum of its non-overlapping parts.

  5. Example 1Area of an Irregular Figure 19 6 Area of irregular figure = area of rectangle – area of triangle + area of semicircle. 6 6 22

  6. IRREGULAR FIGURES ON THE COORDINATE PLANE To find the area of a polygon on the coordinate plane, separate the polygon into known figures.

  7. Example 2Coordinate Plane T(1, 10) 11 10 9 8 S(-3, 7) U(3, 7) 7 6 5 4 3 2 R(-5, 0) V(3, 0) 1 -8 -6 -4 -2 2 4 6 8 -1

  8. Guided Practice 8 3.6 9.2

  9. Guided Practice 16 32

  10. Guided Practice M(0, 5) 5 4 3 2 1 Q(-3, 0) N(3, 0) -6 -4 -2 2 4 6 -1 -2 P(0, -3) -3

  11. Guided Practice 7 6 5 R(0, 4) S(10, 4) 4 3 2 1 -2 2 4 6 8 10 12 T(10, 0) V(0, 0) -1 -2 -3

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