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Comprehensive Guide: Areas of Irregular Figures

Learn to find areas of irregular figures using coordinate planes, auxiliary lines, and area formulas. Examples and homework problems included.

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Comprehensive Guide: Areas of Irregular Figures

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  1. 11.4 Areas of Irregular Figures

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

  3. D E F Areas of Irregular Figures • An irregular figure is a figure that cannot be classified into the specific shapes that we have studied. • Irregular figures are also called composite figures because the region can be separated into smaller regions. • Auxiliary lines are drawn in quadrilateral ABCD. DE, and DF separate the figure into ADE, CDF, and rectangle BEDF

  4. Postulate 11.2 • The area of a region is the sum of all of its nonoverlapping parts.

  5. The figure can be separated into a rectangle with dimensions 6 units by 19 units, a semicircle with a radius of 3 units, and an equilateral triangle with sides each measuring 6 units. º Example 1: • Find the area of the figure. • Use the 30º-60º-90º relationships to find that the height of the triangle is 3Ö3.

  6. Example 1: • Area of irregular figure= • Area of rectangle – area of triangle + area of semicircle = lw – ½ bh + ½ (pi)(r)² Area Formulas = 19(6) – ½(6)(3Ö3) + ½(pi)(3²) Substitution = 114 – 9Ö3 + ½(9)(pi) Simplify Use a calculator = 112.5 units²

  7. T (4, 11) U (6, 7) S (-3, 7) V (6, 0) R (-5, 0) Areas of Irregular Figures on a Coordinate Plane • To find the area of an irregular polygon on the coordinate plane, separate the polygon into known figures.

  8. Example 2: T (4, 11) U (6, 7) S (-3, 7) V (6, 0) R (-5, 0) • Find the area of the shaded region. • Find the difference between x-coordinates to find the length of the base of the triangle and the lengths of the bases of the trapezoid. • Find the difference between the y-coordinates to find the heights of the triangle and trapezoid.

  9. Example 2: Area formulas Substitution Simplify • Area of RSTUV= • Area of STU + area of trapezoid RSUV = ½bh + ½h(b1+b2) = ½(8.1)(4.5) + ½(7)(9+11) = 88.2 units²

  10. Homework • Page 619 #8-15, 16-22 evens CREATED BY: Cecilia Herrera AND Savannah Girlinghouse

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