4th Grade - Formulas For Area And Perimeter

 
     
 
     
 
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4th
Algebra
Formulas for Area and Perimeter
Use and interpret formulas (i.e. area = length x width or A = lw) to answer questions about quantities and their relationships.
Understand the formula to find the area (Area = length x width) and perimeter (Perimeter = 2l + 2w) and make measurements.
 

Sample Problems

(1)

Find the perimeter


(16 cm)

(2)

Find the area: ______



(3 x 10 = 30; 4 x 8 = 32; 30 +32= 62 in2)

(3)

Find the unknown measurement for the perimeter


(30 m)



(4)

Find the unknown width for the area:

(7cm)

(5)

Find the area and the perimeter for the rectangle.


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Area = ____ x ___ = _____


Perimeter = ______ x _____ or _____ + _____ + ______ + _____ = ______


(A= 7 x14= 98 sq. units; P=42 units)

(6)

Use and interpret formulas (i.e. area = length x width or A = lw) to answer questions about quantities and their relationships. (4)

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, have them count the number of squares across (5) and the number of squares down (4). Multiply the numbers and it will also equal the area A = 5 x 4 = 20.



 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(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


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)

Divide figure to find area:

Example


 

 

 4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Divide the polygon into two rectangles. The larger rectangle measures as (4) length and (7) at the width. Use the formula for finding the rectangle (A = l x w) A = 4 x 7 = 28. Next, find the area of the smaller square which is (3) length and (3) width. A= 3 x 3 = 9. Finally, add the two areas together 28 + 9 = 37 sq. units.


(5)

Geo-board/ Dot Paper

Have the child practice drawing shapes and counting the number of squares it covers on the inside. Inform 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.



Extra Help Problems

(1)

Find the perimeter:

(31 in)

(2)

Find the perimeter:


(23 cm)

(3)

Find the perimeter:

(22 m)

(4)

Find the perimeter:


(21 ft)

(5)

Find the perimeter:


(10 yd)

(6)

Find the unknown measurement for the perimeter:


(2 ft)

(7)

Find the unknown measurement for the perimeter:


(4 in)

(8)

Find the unknown measurement for the perimeter:


(10 yd)

(9)

Find the unknown measurement for the perimeter:


(3 cm)

(10)

Find the area: ________


(16 in2)

(11)

Find the area: ________


(50 yd2)

(12)

Find the area:


(3 x 10 = 30; 4 x 8 = 32; 30 + 32 = 62 in2)

(13)

Find the area:


(30 m2)

(14)

Find the unknown width for the area:


(4 in)

(15)

Find the unknown width for the area: p.506-508


(4 ft)

(16)

Find the unknown width for the area:


(4 m)

(17)

Find the area and the perimeter. Are they the same?


(A= 24 cm) (P = 22 cm2) (A= 24 cm2) (P = 28 cm)

Areas are the same; Perimeters are different

(18)

Find the area and the perimeter. Are they the same?

(A = 4 cm2) (P= 8 cm) (A= 4 cm2) (P = 10 cm)

Areas are the same; Perimeters are different

(19)

Find the area and the perimeter. Are they the same?


(A = 12 in2) (P = 14 in) (A = 12 in2) (P= 16 in)

Areas are the same; Perimeters are different

(20)

Find the area and the perimeter. Are they the same?



(P= 18 yd2) (A= 18 yd) (A= 20 yd2) (P= 18 yd)

Perimeters are the same; Areas are different

(21)

Find the area and the perimeter. Are they the same?



(A= 6 cm 2) (P = 10 cm) (A= 6 cm 2) (P= 14 cm)

(22)

Find the area of the figure below:


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Area = ______


(40 sq. units)

(23)

Find the perimeter

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Perimeter = ______

Write two formulas for perimeter: _______________ and _____________


(P =8 x 4= 32 units) (P= 8+ 8 + 8 + 8 =32 units)

(24)

Find the unknown measurement:

Area = 110 cm2

Length= 5 cm

Width = _____ cm


(22 cm)

(25)

Find the unknown measurement:

Perimeter = 40 m

Length = 5

Width = ____


(8 m)

 

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