# 4th Grade - Find Areas Using Squares And Rectangles

 Grade Level: 4th Skill: Area and Perimeter Topic: Find Areas Using Squares and Rectangles Goal: Understand and use formulas to solve patterns involving perimeters and areas of rectangles and squares. Use those formulas to find the areas of more complex figures dividing the figures into basic shapes. Skill Description: Know and understand how to find the area and perimeter of rectangles and squares by using the formulas (i.e. A= l x w; P = 2w + 2l or P = s + s + s). In addition, find the area of complex polygons by dividing the shape into rectangles.

## Building Blocks/Prerequisites

### Sample Problems

(1)

Find the missing measurement for the perimeter of the rectangle:

Perimeter = 22 in.

P = ______ + ______ (2 x 3 + 2 x 8 = 22; missing number is 8 in.)

(2)

Write the formula and solve the area for the square: ________ (A = 3 x 3 =9 sq. units)

(3)

Write the formula and find the area and perimeter for the polygon:

Area: _____________________ (A = 4 x 18 =72 + 6 x 8 = 48; 72 + 48 = 120 ft.2)

Perimeter: _________________ (P = 4 + 10 + 6 + 8 + 10 + 18 =56 ft.)

(4)

Find the unknown length for the area:

Area = 108 sq. units

Length = 12 units

Width = _____ (9 units)

(5)

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

Find the area: ________ (A = 9 x 7 = 63 sq. units)

Find the perimeter: ___________ (P = 2 x 9 + 2 x 7 = 25 units)

### 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.

(2)

Review the formula for area and explain:

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

A= 20 square units

 5 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

 5 4 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).

Polygon- A closed plane figure with straight sides (most shapes, except for circle, oval, and other non-straight line figures).

(4)

Geo-board/ Dot Paper

Have the child practice drawing rectangular figures that have the same area, but different perimeters. 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.

(6)

Divide figure to find area:

Example

 4 4 7 3 3 7

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.

### Extra Help Problems

(1)

Find the perimeter for the figure below: ________

(Perimeter=24in)

(2)

Find the perimeter for the figure below: _________

(Perimeter=26cm)

(3)

Find the perimeter for the figure below: _______

(Perimeter=20m)

(4)

Find the perimeter for the figure below: ________

(Perimeter=56ft)

(5)

Find the area of the figure below: ___________

(Area=20in2)

(6)

Find the area for the figure below: _________

(Area=36yd2)

(7)

Find the area for the figure below: _________

(Area=40m2)

(8)

Find the area and perimeter for the polygon:

Area = ________________ + ______________

Perimeter = ____________

Figure A:

(Area=16yd 2) (Total Area=28yd 2)

Figure B: (Total Perimeter = 32 yd 2)

(Area=12yd 2)

(9)

Find the area and perimeter for the polygon:

Area = ________________ + ______________

Perimeter = ____________

Figure A: ( Total Area=33cm 2)

(Area=7x3=21cm 2)

(Perimeter = 24 cm)

Figure B:

(Area=3x4=12cm 2)

(10)

Find the area and perimeter of the polygon:

Figure A: (Total Area=39cm 2)

(Area=3x3=9cm 2)

(Perimeter = 28 cm)

Figure B:

(Area=5x6=30cm 2)

(11)

Find the area and perimeter for the rectangle:

(Area=30 yd 2)

(Perimeter=22 yd)

(12)

Find the area and perimeter for the rectangle:

Area = _____________

Perimeter = ____________

(Area=48 in 2)

(Perimeter=32 in)

(13)

Find the area and perimeter for the polygon:

Area = _____________

Perimeter = ____________

Figure A:

(Area-7x2=14ft2)

Figure B:

(Area-4x3=12ft2)

(Total Area=26ft2 ) (Perimeter = 26 ft.)

(14)

Find the area and perimeter of the rectangle

Area = _____________

Perimeter = ____________

(Area=40m)

(Perimeter=26m)

(15)

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

Area: _____ (A= 8 x 2 = 16 sq. units)

Perimeter: ______ (P = 2 x 8 + 2 x 2 = 20 units)

(16)

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

Find the area: ________ (A = 12 x 11 = 132 sq. units)

Find the perimeter: ___________ P = (12 x 2 + 11 x 2 = 46 units)

(17)

The area is: 20 cm 2 The perimeter is 24 cm

Write the formulas for the area and perimeter

A= ___ x ____ = ____ (A = 10 x 2 = 20 cm 2)

P= _____ + ______ = _____ (P = 2 x 10 + 2 x 2 = 24 cm)

(18)

The area is: 50 in 2 The perimeter is 54 in.

Write the formulas for the area and perimeter

A= ___ x ____ = ____ (A = 25 x 2 = 50 in 2)

P= _____ + ______ = _____ (P = 25 x 2 + 2 x 2 = 54 in.)

(19)

The area is: 28 ft 2 The perimeter is 22 ft

Write the formulas for the area and perimeter

A= ___ x ____ = ____ (A = 7 x 4 = 28 ft. 2)

P= _____ + ______ = ______ (P = 2 x 7 + 2 x 4 = 22 ft.)

(20)

The area is: 80 yd 2 The perimeter is 84 yd

Write the formulas for the area and perimeter

A= ___ x ____ = ____ (A = 40 x 2 = 80 yd 2 )

P= _____ + ______ = ______ (P = (2 x 40 + 2 x 2 = 84 yd.)

(21)

Write the formula and find the missing measurement:

Perimeter = 72 m

P = (2 x 25 + 2 x 11 = 72m—missing side = 11m)

(22)

Write the formula and find the missing measurement

(Hint: A square has equal sides)

Area = ___________ (A = 4 x 4 = 16 in. 2)

(23)

Find the missing measurement and write the formula:

Area = 11 cm2

Width = 1cm

Length = ______ (11 cm)

Formula: ______________

(A = 11 x 1 = 11 cm2)

(24)

Find the missing measurement and write the formula:

Perimeter = 12 cm

Side 1 = 4 cm

Side 2 = 3 cm

Side 3 = _______ (5 cm)

Formula: ______________

(P = 4 + 3 + 5 = 12 cm)

(25)

Find the missing measurement and write the formula:

Area = 238 ft. 2

Length = 14 ft.

Width = ______ (17 ft.)

Formula: _________________

(Area = 14 x 17 = 238 ft2)