11.4 Areas of Irregular Figures

ObjectivesFind areas of irregular figures.Find areas of irregular figures on the

coordinate plane.

Areas of Irregular FiguresAn 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

D

F

E

Postulate 11.2The area of a region is the sum of all

of its nonoverlapping parts.

Example 1:

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.

Find the area of the figure.

º

Use the 30º-60º-90º relationships to find that the height of the triangle is 3Ö3.

Area of irregular figure=

Example 1:

= lw – ½ bh + ½ (pi)(r)²= 19(6) – ½(6)(3Ö3) + ½(pi)(3²)= 114 – 9Ö3 + ½(9)(pi)

= 112.5 units²

Area of rectangle – area of triangle + area of semicircle

Area Formulas

Simplify

Use a calculator

Substitution

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.

S (-3, 7) U (6, 7)

T (4, 11)

R (-5, 0)

V (6, 0)

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)

Example 2:• Find the area of the shaded region.

Example 2: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

Homework

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