Section 4 Day 2 - Mosinee School District

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11-4 Objectives

You will learn to:

Find the areas of irregular figures on the

coordinate plane.

Vocabulary

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Postulate

Irregular Shape

To estimate the area of

an irregular shape, you

can sometimes use a

composite figure.

First, draw a composite

figure that resembles the

irregular shape.

Then divide the composite figure into

simple shapes.

Estimating Area

Use a composite figure to estimate the shaded

area. The grid has squares with a side length

of 1 ft.

Draw a composite figure that

approximates the irregular

shape. Find the area of each

part of the composite figure.

area of triangle a:

Example Continued

area of triangle b:

area of rectangle c:

A = bh = (2)(1) = 2 ft 2

area of trapezoid d:

Area of composite figure: 1 + 0.5 + 2 + 1.5 = 5 ft 2

The shaded area is about 5 ft 2 .

Find the area of polygon MNPQR.

First, separate the figure into

regions. Draw an auxiliary

line perpendicular to

from 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.

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.

Area

formulas

Substitution

Simplify.

Answer: The area of polygon MNPQR is 44.5

square units.

Find the area of polygon ABCDE.

Answer:

Your Turn

Use a composite figure to estimate the shaded

area. The grid has squares with side lengths of

1 ft.

Draw a composite figure that

approximates the irregular

shape. Find the area of each

part of the composite figure.

Your Turn

area of triangle:

area of half circle:

area of rectangle:

A = lw = (3)(2) = 6 ft 2

The shaded area is about 12 ft 2 .

Lesson Quiz

Use a composite figure to estimate the

shaded area. The grid has squares with side

lengths of 1 cm.

Area = ½(1)(1)(2) = 1

Area = (1)(2) = 2

Area = ½(2)(4) = 4

Area = ½(1)(3) = 1.5

Area = ½(1)(1) = .5

about 9 cm 2

What did you learn today

How to:

Find the areas of irregular figures

on the coordinate plane.

Assignment:

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