Area and Perimeter Word Problems and Open-Ended Questions


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Name                                              Class

1. Buying Carpet

Mrs. Ames wants to buy carpet for the room shown below.

How much carpeting does she need to buy to cover the floor area?  
a.  140 sq. ft.
b.  92 sq. ft.
c.  48 sq. ft.
d.  24 sq. ft.

 

2. More Area and Perimeter

 Carefully examine each of the three rectangles shown below.

 

 

 

 

 

A

 

 

 

 

 

 

 

 

 

 

 

 

B

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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 D

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
                                             
                                             
                                             
                                             

                                                                               = 1 square cm

Calculate the perimeter and the area of each rectangle above. Label each answer.

RECTANGLE PERIMETER AREA
A
B
C
D

 

3. Area and Perimeter

 Carefully examine each of the three rectangles shown below.

 

 

 

 

 

  

 

 

 

 

 

 

 

 

  

 

 

 

 

 

 

 

 

 

  

A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

 

 

 

B

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 C

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                                                                               = 1 square unit

  • Each rectangle represents the backyard of a house. Which house has the most land?

  • Which house would need to buy the most fencing material to completely enclose the yard?

  • Show or explain how you got your answer.

 

 

4. And Even More Area and Perimeter Practice

Examine rectangles A, B, and C below.
Calculate the perimeter and the area of each one.
Complete the chart below. Don't forget to label your answers.

6 ft.

A
 

                                         7ft.

 

 

 

2 in.

 

B

 

 5 in.
 
 

                C

                             25 in.
RECTANGLE PERIMETER AREA
A
B
C

 

5. Covering Box Tops with Paper
The pink and orange rectangles below are the tops of gift boxes.
You want to cover each of them with fancy paper.

  • Which box top, the pink or the orange will require more paper? 

  • How much more paper will you need to use?

   

33 cm

  

2 cm

  
   

 

12 cm

  
 

5 cm

    

6. Measuring Geometric Objects

  =  1 square centimeter

What is the area of the shape on the grid?       Need help?
A. 16 square centimeters
B. 18 square centimeters
C. 20 square centimeters
D. 22 square centimeters

                                  7.  Jerome's Design                                          

What is the area of Jerome's design? 

72 square feet
39 square feet
38 square feet
34 square feet

 

 

                    8. Painting the Floor                         

What is the area of the shaded part of the floor? 

   

 

9. The Window Frame
A window frame in the shape of a rectangle is 90 centimeters long and 40 centimeters wide.rectangular window: 90 centimeters long and 40 centimeters wide
What is the perimeter of the window frame?
 A.   50 cm
 B.   130 cm
 C.   260 cm
 D.   360 cm

 

                          10. Jewelry Box                    

Beth is making a lid for her jewelry box with square tiles, as shown below.
jewelry-box lid
What is the area of Beth’s jewelry-box lid? 
  A. 6 square inches
  B. 10 square inches
  C. 12 square inches
  D. 24 square inches

 

11. Open Ended Question

  • Be sure to answer and label all parts of the question.

  • Show all your work (tables, drawings, computations, etc.)

  • If you do the work in your head, explain in writing how you did the work.

Chester drew the shaded figure on the grid paper shown below.
  • What is the area, in square centimeters, of the shaded figure on Chester's grid? Show or explain how you got your answer.
  • Chester drew a rectangle that had the same area as the shaded figure on the grid above. what could be the dimensions (length and width) of the rectangle he drew? Show or explain how you got your answer.
  • Is there a different rectangle that Chester could have drawn that has the same area as the shaded figure on the grid above? show or explain how you got your answer.

Answer:
 

       

12. Largest Area

                                Answer:

Explain how you got your answer.

 

13. The Garden Fence

Answer:

14. Area of the figure

What is the area of this figure?      Answer:

   

 A. 58 ft2
 B. 108 ft2
 C. 198 ft2
 D. 208 ft2

15. Comparing Perimeters

Look at the rectangles below.
The perimeter of rectangle Y is how many centimeters greater than the perimeter of rectangle Z?
  2 cm
  4cm
  6 cm
  8 cm

Explain how you got your answer.

16. Tough Question

On hot summer days, much unwanted heat enters the home through the roof, walls, and glass. There are several ways to deal with this:

Roofs and walls are best protected by using insulation and vegetation. Vegetation, such as trees and shrubs, can really help to protect the home by preventing sunlight from directly hitting it.

 

ma-p101
 
You live in a rectangular shaped home that is 75 feet long and 50 feet wide. You want to plant shrubs around the home to help protect the exterior walls from direct sunlight. You are to plant the shrubs 3 feet apart. Approximately how many shrubs will you need to surround the house? (Round to the nearest whole number.)
 
ANSWER (with label): 

Explain how you got your answer:
 

17. Really Tough Question

Your local home builder can make solar screens for your home. They can be used to cover the windows to block the sunlight and the heat. The builder needs to know how many square feet of screening to purchase. The windows you wish to cover are as follows:


 

    Two 3' × 5'          
 		 Two 3' x 6'              
 		 Three 3' x 3'

 

How many square feet of solar screening must be purchased? 
 
If the screening is sold in rolls of 50 square feet, how many rolls of screening are needed? 
 
Explain how you got your answers: