1. 11.4 Areas of Irregular Figures

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

3. 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. D F E
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. 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: = 112.5 units² = lw – ½ bh + ½ (pi)(r)² Area Formulas
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
= units²

7. Areas of Irregular Figures on a Coordinate Plane
V (6, 0)
To find the area of an irregular polygon on the coordinate plane, separate the polygon into known figures.

8. Example 2: 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.
S (-3, 7)
U (6, 7)
T (4, 11)
R (-5, 0)
V (6, 0)

9. Example 2: = 88.2 units² Area of STU + area of trapezoid RSUV
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
Area formulas
Substitution
Simplify

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