6th Grade Math Textbook, Fundamentals

Lesson 10-9 for exercise sets. &KDSWHU 

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Find the area of the shaded region. If necessary, round to the nearest tenth.

4.Discuss and Write Describe two different

ways you can use polygons to estimate the

area of the state of Nebraska. Illustrate

each of your answers.

P

P

LQ

LQ

LQ

20 km LQ

You can also find an unknown measurement,

given the area of a complex figure.

Figure MNPQRSTUhas an area

of 873 square feet. What is the

length of side NP?

As with finding the area of a complex

figure, identify the different shapes in

the figure.

Then find the area of each shape.

The sum of these areas is 873 ft^2.

Use this information to write an equation

and solve for x.

702  19 x  873

702  702  19 x 873  702 Subtract 702 from both sides.

19 x 171 Simplify.

 Divide both sides by 19 to isolate x.

x 9 Simplify.

So the length of side NPis 9 feet.

171

19

19 x

19

Key Concept

Area of Complex Figures

When solving area problems

with complex figures:

• Identify shapes that create
  the figure.


• Use formulas for area to find
  each shape’s area.


• Find the sum (or difference)
  of the areas, as necessary.


• If given a total area, use it in
  an equation, and solve for
  the unknown.

IW

IW

IW

xIW

IW

N R

M

U

S

T

P Q

Figure MNPQRSTUcan be formed from

rectangle MSTU and rectangle NPQR.

Area of rectangle MSTU 54 • 13  702

Area of rectangle NPQR 19 •x  19 x