# 4th Grade - Same Area, Different Perimeters

 Grade Level: 4th Skill: Area and Perimeter Topic: Same Area, Different Perimeters 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: Recognize the difference between area and perimeter for rectangles. Understand that rectangles that have the same area may not have the same perimeter.

## Building Blocks/Prerequisites

### Sample Problems

(1)

Find the area and perimeter of the figure:

Area: ____

Perimeter: _______

(A= 27 cm; P = 24 cm)

(2)

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

Figure 1

8 in

Perimeter: ____

Figure 2

Perimeter: ______________

(Figure 1: 28 in; Figure 2: 32 in.)

(3)

Find the area and perimeter:

Area: ____

Perimeter: _____

(A = 94 sq. units; P= 60 units)

(4)

The area is: 72 The perimeter is 34

Write the formulas and draw the figure:

A= ___ x ____ = ____

P= _____ + ______ =

(A = 9 x 2; P = (2 x 9 + 2 x 8=34)

(5)

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

Find the area: ______

Find the perimeter: __________

(A= 9 x6 = 54 sq. units; P= (2 x 9 + 2 x 6= 30 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.

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

 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).

(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.

### Extra Help Problems

(1)

Find the area and perimeter of the figure below:

(Area=32cm)

(Perimeter=24cm)

(2)

Find the area and perimeter of the figure below:

(Area=81cm)

(Perimeter=36cm)

(3)

Find the area and perimeter of the figure below:

(Area=224ft)

(Perimeter=60ft)

(4)

Find the area and perimeter of the figure below:

(Area=54ft)

(Perimeter=42ft)

(5)

Find the area and perimeter of the figure below:

(Area=84in)

(Perimeter=38in)

(6)

Find the area and perimeter of the figure below:

(Area=65m)

(Perimeter=36m)

(7)

Find the area and perimeter of the figure below:

(Area=323in)

(Perimeter=72in)

(8)

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

Figure 1

Area= _______ (24m)

Perimeter=______ (22m)

Figure 2

Area= _____ (24m)

Perimeter= ____ (20m)

(No, different perimeter)

(9)

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

Figure 1

Area= ______ (36in)

Perimeter= ____ (24in)

Figure 2

Area= _____ (36in)

Perimeter= _____ (26in)

(No, different perimeter)

(10)

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

Figure1

Area= _____ (12cm)

Perimeter= ______ (14cm)

Figure2

Area= ______ (12cm)

Perimeter= _____ (16cm)

(No, different perimeter)

(11)

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

Figure1

Area= ______ (18yd)

Perimeter= _____ (18yd)

Figure2

Area= _______ (18yd)

Perimeter= ____ (22yd)

(No; different perimeter. Figure 1 has the same area and perimeter for the rectangle)

(12)

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

Figure1

Area= ____ (30ft)

Perimeter= ____ (22ft)

Figure2

Area= ______ (300ft)

Perimeter= _____ (80ft)

(NO, different perimeters)

(13)

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

Figure1

Area= _____ (15cm)

Perimeter=_____ (16cm)

Figure2

Area= ______ (15cm)

Perimeter= _____ (32cm)

(No, different perimeters)

(14)

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

Figure1

Area= ______ (16m)

Perimeter= _____ (20m)

Figure2

Area= ______ (16m)

Perimeter= ____ (16m)

(No, the two figures have different perimeters. Figure 2 has the same area and perimeter)

(15)

Find the area and perimeter of the figure:

Area: _____

Perimeter: ______

(Area = 36 sq. units; Perimeter = 30 units)

(16)

Find the area and perimeter of the figure:

Area: ______

Perimeter: ______

(Area = 36 sq. units Perimeter = 36 units)

(17)

The area is: 20 The perimeter is 24

Write the formulas for the area and perimeter

A= ___ x ____ = ____

P= _____ + ______ =

(Area= 10 x 2= 20; Perimeter = (2 x 10 + 2 x 2 = 24)

(18)

The area is: 50 The perimeter is 54

Write the formulas for the area and perimeter

A= ___ x ____ = ____

P= _____ + ______ =

(Area= 2 x 25; Perimeter = (2 x 25 + 2 x 2 = 54)

(19)

The area is: 28 The perimeter is 22

Write the formulas for the area and perimeter

A= ___ x ____ = ____

P= _____ + ______ =

(Area = 7 x 4; Perimeter = (2 x 7 + 2 x 4= 22)

(20)

The area is: 80 The perimeter is 84

Write the formulas for the area and perimeter

A= ___ x ____ = ____

P= _____ + ______ =

(Area = 40 x 2; Perimeter = (2 x 40 + 2 x 2= 84)

(21)

The area is: 36 The perimeter is 30

Write the formulas for the area and perimeter

A= ___ x ____ = ____

P= _____ + ______ =

(Area = 12 x 3; Perimeter = (2 x 12 + 2 x 3 = 30)

(22)

The area is: 90 The perimeter is 66

Write the formulas and draw the figure:

A= ___ x ____ = ____

P= _____ + ______ =

(Area= 30 x 3; Perimeter = 2 x 30 + 2 x 3= 66)

(23)

Write the formula for two figures that have the same area, but different perimeters:

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

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

(24)

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

(25)

Explain the difference between area and perimeter. ________________

(Area measures the inside of the figure in square units; Perimeter measures the distance around the figure).