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11.4 Areas of Irregular Figures

11.4 Areas of Irregular Figures. Schyler Ridgeway & Cody Lee. Objectives. Find areas of irregular figures. Irregular Figures. Irregular figure – A figure that cannot be classified as one polygon.

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11.4 Areas of Irregular Figures

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  1. 11.4 Areas of Irregular Figures Schyler Ridgeway & Cody Lee

  2. Objectives • Find areas of irregular figures

  3. Irregular Figures • Irregular figure – A figure that cannot be classified as one polygon. • To find the area of an irregular figure, separate the figure into nonoverlapping shapes of which we can find the area.

  4. Things to Know • Postulate 11.2 - The area of a region is the sum of all of its nonoverlapping parts. • Areas • Area of a Circle – πr^2 • Area of a Triangle - ½bh • Area of a Trapezoid – (b1 +b2)h

  5. º Example 1: • Find the area of the figure • 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. • 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 Simplify = 114 – 9Ö3 + ½(9)(pi) Use a calculator = 112.5 units²

  7. Example 2: • Find the area of polygon MNPQR. 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). This divides the figure into triangle MRS, triangle NKM, trapezoid POKN and trapezoid PQSO.

  8. Example 2: • 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.

  9.  Area formulas Substitution Simplify. Example 2: Answer: The area of polygon MNPQR is 44.5 square units.

  10. Assignment: • Pre-AP Geometry: Pg. 619 #8 – 23

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