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# Area and Perimeter of Rectangles

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### Introduction

Susan loves to draw.  Her parents want to get her a table for her room so she can have her own drawing station.  Her parents have narrowed it down to two possibilities.  They cannot make a decision until they know the largest size paper that Susan uses for her drawings.

The first desk is 45 in x 28 in.  It looks like a wooden table and would look great in her room.

Source: http://www.clker.com/

[Figure1]

The second desk is a square table.  Each side measures 26 inches.

Source: http://www.clker.com/

[Figure2]

After looking at some of Susan's drawings, her parents found out some of the largest paper she uses is about 24 inches long and has a width of 16 inches.

Her parents need help finding the perimeter and area of each of the tables.  After that, they need to make a decision on which table to purchase.

### Guided Learning

The area means the amount of space inside a two-dimensional figure. To find the area of a rectangle calculate the product of its base (length) and height (width)  $A=bh$ .  As fifth graders, we are more familiar with the area of a rectangle being length x width or $A=lw$ , but it is important to understand that the concept is the same.

Remember that perimeter is the distance around a two-dimensional figure.  In the past you may have learned that you can find the   perimeter of any shape by adding all the sides together.   There is an easier way, however, when you are dealing with a rectangle .  We know that the opposite sides are congruent.  Therefore, we can use the formula  $P=2b+2h$ , where $b$ is the base (or length) and $h$ is the height (width).

#### Example A

Find the area and perimeter of a rectangle with sides 4 cm by 9 cm.

The perimeter = 2b + 2h

P= 2(__) + 2 (__)

P= ____+____

P=_____

The area is Length (base) x Width (height)

A= ____ x_____

A= _____ cm 2

#### Example B

Find the area and perimeter of a rectangle with sides 13 m and 12 m.

P=

A=

Watch this video for help with the Examples above.

#### Let's go back and help Susan's parents.

The dimensions of table 1 were 45 in x 28 in.

Table 2 was a square.  Each side was 26 in.

What is the perimeter and area of table 1?

Perimeter= 2(b) + 2(h)

Area=length x width

What is the perimeter and area of table 2?

Perimeter=2(__) + 2(__)

Area= ___ x ____

Which table would you recommend to Susan's parents?  Why?

.

### Practice Set

1. Find the area and perimeter of a square with sides of length 10 in.
2. Find the area and perimeter of a rectangle with width of 9 cm and length of 3 cm.
3. Find the area and perimeter of a rectangle if the width is 8 in and the length is 7 in.
4. Find the area and perimeter of a square if the sides are 4 ft.
5. If the area of a square is 36 ft 2 , find the perimeter.
6. If the perimeter of a square is 20 in, find the area.
7. The perimeter of a rectangle is 48. Find two different dimensions that the rectangle could be.
8. Draw two different rectangles that haven an area of 40 mm 2 .
9. Your grandma gave you a frame with a picture of you and her at Disney World.  The frame was  10in x 12in.  How much space did it take up on the wall?
10. Mr. Goebel was sorting books to give to his class.  He was setting them on his desk.  He wanted make sure he could set 1 book on his desk for each kid.  His desk dimensions were 64 in x 30 in.  The books were 8in x 5in.  Without stacking them on top of each other, how many books could fit on his desk?  If he has 25 kids in his class, can he fit enough for each kid to get one?  Explain.

For problems 11 and 12 find the dimensions of the rectangles with the given information.

1. A rectangle with a perimeter of 16 units and an area of 15 units 2 .
2. A rectangle with a perimeter of 24 units and an area of 32 units 2 .
3. The length of a rectangle is 2 times the width. The width is 8 cm.  What is the area and the perimeter?
4. The length of a rectangle is 2 less than 2 times the width. The width is 10.  What is the area and the perimeter?

### Review

• Area means the amount of space inside a two-dimensional figure. To find the area of a rectangle calculate the product of its base (length) and height (width)  $A=bh$ .  As fifth graders, we are more familiar with the area of a rectangle being length x width or $A=lw$ .
• Perimeter is the distance around a two-dimensional figure.
• You can find the  perimeter of any shape by adding all the sides together To find the perimeter of a rectangle we can use the formula  $P=2b+2h$