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.

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 D C B

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 F B

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

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

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

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

Guided Practice 8 3.6 9.2

Guided Practice 16 32

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

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