6th Grade Math Textbook, Fundamentals

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Problem Solving: Review of Strategies

Objective To solve problems using a variety of strategies

Problem: The corresponding sides of the right triangles below
are parallel. All three pairs of sides are the same distance apart.
What is the area of the shaded region?

Read to understand what is being asked.

List the facts and restate the question.

Facts: A right triangle with legs of length 6 meters

and 8 meters is inside a right triangle with

legs of length 12 meters and 16 meters.

Corresponding sides of the two triangles

are parallel and the same distance apart.

Question:What is the area of the region between

the triangles?

Select a strategy.

You can use the strategy Reason Logicallyand regard the area

of the region as the difference in areas of the two triangles.

You can also use the strategy Adopt a Different Point of View

and consider moving the inside triangle to a new location.

Apply the strategy.

Method 1:Reason Logically

A right triangle with legs of length aand bhas area Agiven by A ab.

Therefore, the area of the larger right triangle is

AL (12 m)(16 m) 96 m^2.

The area of the smaller right triangle is

AS (6 m)(8 m) 24 m^2.

So the area of the shaded region is

A96 m^2 24 m^2 72 m^2.

1

2

1

2

1

2

16 m

6 m

12 m

8 m

12-9

Problem-Solving Strategies

1.Guess and Test

2.Organize Data

3.Find a Pattern

4.Make a Drawing

5.Solve a Simpler Problem

6.Reason Logically

7.Adopt a Different Point of View

8.Account for All Possibilities

9.Work Backward

10.Consider Extreme Cases