4th Grade - Same Perimeter, Different Areas

 
     
 
     
 
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4th
Area and Perimeter
Same Perimeter, Different Areas
Understand that rectangles that have the same perimeter can have different areas.
Recognize the difference between area and perimeter for rectangles. Understand that rectangles that have the same perimeter may not have the same area.
 

Sample Problems

(1)

Find the area and perimeter of the figure:

Area: ________ (256 cm2)

Perimeter: ________ (64 cm)

(2)

Do the figures with the same perimeter have the same area?

Figure 1

Area: _____ (12 in2.)

Perimeter: _____ (14 in.)


Figure 2


Area: ___________ (10 in.)

Perimeter: ________ (14 in)


Are the areas the same? ________ (no)


(3)

Find the area and perimeter:

Area: _____ (72 units)

Perimeter: _______ (30 units)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(4)

The area is: 90 in The perimeter is 38 in

Write the formulas and draw the figure:

A= ___ x ____ = ____ (10 x 9 = 90 in2)


P= _____ + ______ = (2 x 9 + 2 x 9 = 38 in.)


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(5)

Use the figures below to write the formula for perimeter and area.

Find the area (A): ________ (54 sq. units)

Find the area (B): ________ (56 sq. units)

Find the perimeter (A): ___________ (30 units)

Find the perimeter (B): ____________ (30 units)

How are they similar? _________________ (same perimeter)


A














B







 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 













 

 

 

 

 

 

 

 

 

 













 

 

 

 

 

 

 

 

 

 













 

 

 

 

 

 

 

 

 

 













 

 

 

 

 

 

 

 

 

 













 

 

 

 

 

 

 

 

 

 













 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 























 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Learning Tips

(1)

Place the shape on a grid and have child count the shaded squares. Let them know that is the area for the figure (the colored surface that covers the inside of the shape).

Then, review that the squares that outline the shape is the perimeter.


Have the child practice with the grid paper by having them draw figures and color them with the same area and different perimeters (you can begin by giving them the area and perimeters. Gradually, let them make the shapes independently.

(2)

Review the formula for area and explain:

Area = Length x Width (A= l x w) A = 5 x 4

A= 20 square units


 


 

 

 

 

 

 

 

 

 

 

 

 4

 

 

 

 

 

Perimeter = 2 x width + 2 x length (P = 2W x 2L)

P = (addition of # of sides)

P = (2 x 5) + (2 x 4)

P = 18


 


 

 

 

 

 

 

 

 

 

 

 4

 

 

 5

 

 

(3)

Math vocabulary:

Perimeter- The distance around a figure; measured in linear units.


Area- The number of square units used to cover the surface of the figure


Square unit- a square with a side length of one unit; used to measure area (i.e. cm2).

(4)

Geo-board/ Dot Paper

Have the child practice drawing rectangular figures that have the same perimeter, but different area. Have them label the length, width, area, and perimeter. Discuss the differences on how they look.

Remind them that the number of squares it covers is the area in square units. The number of squares on that outlines the shape is the perimeter.




(5)

Practice math facts (multiplication and addition) to solve simple measurements for area and perimeter.

Extra Help Problems

(1)

Find the area and perimeter of the figure below:

Area __________ (27 m2)

Perimeter __________ (24 m)









(2)

Find the area and perimeter of the figure below:

Area: ______________ (72 yd2)

Perimeter: ___________ (34 yd)

(3)

Find the area and perimeter of the figure below:

Area: ____________ (48 cm2)

Perimeter: ___________ (38 cm)








(4)

Find the area and perimeter of the figure below:

Area: ____________ (252 m2)

Perimeter: ___________ (64 m)



(5)

Find the area and perimeter of the figure below:

Area: _______________ (91 in2)

Perimeter: ______________ (40 in)









(6)

Find the area and perimeter of the figure below:


Area: ___________ (60 cm2)

Perimeter: _____________ (34 cm)







(7)

Find the area and perimeter of the figure below:

Area: ____________ (360 yd2)

Perimeter: ___________ (76 yd)

(8)

The figures below have the same perimeter. Do they have the same area?

Figure 1

Area: _______________ (15 in2)

Perimeter: _____________ (16 in)


Figure 2


Area: _________ (7 m2)

Perimeter: ________ (16 m)


Are the areas the same: _____ (no)










(9)

The figures below have the same perimeter. Do they have the same area?


Figure 1


Area: _______ (16 cm2)

Perimeter: _________ (16 cm)


Figure 2

Area: ________ (12 yd2)

Perimeter: __________ (16 yd)


Are the areas the same? __________ (No)













(10)

The figures below have the same perimeter. Do they have the same area?


Figure1

Area: ________ (24 in2)

Perimeter: _________ (20 in)


Figure2



Area: ________ (25 in2)

Perimeter: ________ (20 in.)


Are the areas the same? _________ (no)










(11)

The figures below have the same perimeter. Do they have the same area?

Figure1


Area: _______ (32 yd2)

Perimeter: _________ (24 yd)



Figure2



Area: __________ (20 yd2)

Perimeter: __________ (24 yd)


Are the areas the same? ____________ (no)





(12)

The figures below have the same perimeter. Do they have the same area?

Figure1

Area: _________ (18 m2)

Perimeter: ___________ (18 m)


Figure2



Area: ____________ (14 m2)

Perimeter: ___________ (18 m)


Are the areas the same? __________ (no)


(13)

The figures below have the same perimeter. Do they have the same area?

Figure1

Area: ______ (200 in2)

Perimeter: ________ (60 in)


Figure2


Area: ________ (125 in2)

Perimeter: _______ (30 in)


Are the areas the same? _______ (no)


(14)

The figures below have the same perimeter. Do they have the same area?

Figure1

Area: ________ (42 cm2)

Perimeter: _______ (26 cm)


Figure 2

Area: ______ (36 cm2)

Perimeter: ______ (26 cm)


Are the areas the same? _______


(15)

Find the area and perimeter of the figure:

Area: _____ (18 sq. units)

Perimeter: ______ (18 sq. units)


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 







(16)

Find the area and perimeter of the figure:

Area (A): ______ (16 sq. units)

Area (B): ______ (25 sq. units)

Perimeter (A): ______ (20 units)

Perimeter (B): ______ (20 units)

How are the figures the same? (same perimeter)

A

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

 

 

 

 






 

 

 

 

 


 

 

 

 

 

 






 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 




















(17)

The area is: 15 m The perimeter is 16 m

Write the formulas for the area and perimeter

A= ___ x ____ = ____ (5 x 3 = 15 m2)


P= _____ + ______ = (2 x 5 + 2 x 3 = 16 m)


(18)

The area is: 32 The perimeter is 24

Write the formulas for the area and perimeter

A= ___ x ____ = ____ (8 x 4 = 32 in2)


P= _____ + ______ = (2 x 8 + 2 x 8 = 32 in)


(19)

The area is: 63 cm The perimeter is 32 cm

Write the formulas for the area and perimeter

A= ___ x ____ = ____ (9 x 7= 63 cm2)


P= _____ + ______ = (2 x 9 + 2 x 9 = 32 cm)



(20)

The area is: 18 The perimeter is 22

Write the formulas for the area and perimeter

A= ___ x ____ = ____ (9 x 2 = 18 cm2)


P= _____ + ______ = (2 x 9 + 2 x 2 = 22 cm)



(21)

The area is: 40 The perimeter is 28

Write the formulas for the area and perimeter

A= ___ x ____ = ____ (10 x 4 = 40 in2)


P= _____ + ______ = (2 x 10 + 2 x 4 = 28 in)



(22)

The area is: 66 The perimeter is 70

Write the formulas and draw the figure:

A= ___ x ____ = ____ (33 x 2 = 66 yd2)


P= _____ + ______ = (2 x 33 + 2 x 2 = 70 yd)





(23)

Write the formula for two figures that have the same perimeter, but different areas:


Figure 1: A = _____ x _____ P= ________ + __________


Figure 2: A = ______ x ______ P= ________ + ___________


(answers will vary)

(24)

Draw two figures with the same perimeters, but different areas:


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(25)

Explain the difference between area and perimeter.

(area measures the surface of the figure; perimeter measures the outside of the figure)

 

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