Lesson 2.2.2 Concept: Square Units and Area of Rectangles Vocabulary: length - The distance from one end of an object to the opposite end. (linear measure) dimensions -A flat region or space that tells how far a figure extends in each direction. (plane) (For example, the dimensions of a rectangle might be 16 cm wide by 7 cm high.) plane - A plane is a two-dimensional flat surface that extends without end.  It is made up of points and has no thickness. 7cm 16 cm

How many ways can we measure the area? plane - A plane is a two-dimensional flat surface that extends without end.  It is made up of points and has no thickness. When communicating measurements, it is important to be clear about the unit of measure that you are using.  In other words, saying that you are “30 tall” or that a swimming pool is “8 big” tells you very little.  Today you will learn about units of measurement for area that are often used.  As you work, keep these questions in mind: How many ways can we measure the area? What is the unit?

29. BE THERE, OR BE SQUARE As you have seen, area can be measured using units of many different shapes and sizes.  However, area is most easily and most often measured in “square units.”  The diagram at right is a picture of “one square unit.”  A square unit can be many different sizes, and it is named for the unit of measure used for its side length (linear measure) .  For example, if a unit is square with a length of one foot on each side, then the square unit is called “one square foot.” What would you call a square unit that measures one centimeter on each side?  One inch on each side?  One yard on each side?  One mile on each side?  With a ruler, draw a picture of two of the square units described in part (a) that will fit on your notebook paper.  Your drawings should be accurate, so measure carefully.   The units “square inches” can also be written in a shorter way as “in2.”  This is read as “inches squared.”  The small 2 is an exponent indicating that the units are a square.  Write the units of “square centimeters” and “square feet” using the same format.

30. NATHANIEL’S PATIO Nathaniel decided to tile his rectangular patio with square tiles.  He had 14 blue square tiles and wanted to lay them throughout the area to make a design.  He set the tiles inside the patio border as shown in the diagram at right.  Now he needs your help to figure out how many white tiles (of the same size) he needs to finish the job. What is the total area of Nathaniel’s patio as measured in patio tiles?  With a diagram, explain how you arrived at your answer.  How many white tiles does he need to finish the job?  You can assume that the white tiles are the same size and shape as the blue tiles.  If the sides of the square tiles are 1 foot long, what are the dimensions (the length and width) of Nathaniel’s patio?  What is the area of the patio (using correct units)? 

31. The area of a rectangle is the number of square units (all of the same size) that completely fill the inside of the rectangle without gaps or overlaps. How many square centimeters will fill a rectangle that is 5 centimeters by 3 centimeters?  Sketch the situation.   How many square inches will fill a rectangle 6 inches by 2 inches?  Sketch the situation.   How many square feet will cover a rectangle 60 feet by 20 feet?  Sketch the situation.  Explain how you determined your answer.  What is the area of a rectangular garden that is 60 feet by 20 feet? 

33. Consider the figure below 33. Consider the figure below.  (Note that all corner angles are right angles.) Find the area of the figure at right in at least two different ways.  Justify how you get your answer with diagrams and remember to label them with the correct units.  Find the perimeter of the figure.

Tonight’s homework is… 2.2.2 Review & Preview, problems #34-#38. (text page 70) Label your assignment with your name and Lesson number in the upper right hand corner of a piece of notebook paper. (Lesson 2.2.2) Show all work and justify your answers for full credit.