practice lesson 30 connect area and perimeter b m€¦ · practice lesson 30 connect area and...

125©

Cu

rriculu

m A

ssociates, LL

C

Copyin

g is not perm

itted.

Practice Lesson 30 Connect Area and Perim

eterU

nit 5

Practice and Prob

lem Solvin

gU

nit 5 Measurem

ent and D

ata

Key

B Basic M Medium C Challenge

©Curriculum Associates, LLC Copying is not permitted.322 Lesson 30 Connect Area and Perimeter

Solve.

4 The diagram shows the fl oor space of two diff erent tents. Which tent’s fl oor has the greater area?

8 feet

Tent A 8 feet

9 feet

Tent B 7 feet

Show your work.

Solution:

5 Draw a rectangle that is 5 units long and 4 units wide. Show how to fi nd the area.

6 Liv draws a rectangle with the same area as the one you drew for problem 5, but a diff erent length. What is a possible length and width of Liv’s rectangle? Explain.

7 The shaded rectangle is 8 units long and 6 units wide. The larger rectangle is 10 units long and 8 units wide. What is the area of the white space around the shaded rectangle?

Show your work.

Solution:

The area of the white space is the difference between the two areas.

322

Possible work: Tent A: 8 3 8 5 64 square feet;

Tent B: 9 3 7 5 63 square feet.

Possible work: large rectangle: 10 3 8 5 80 square units; shaded rectangle: 8 3 6 5 48 square units; subtract to find the area of the white space: 80 2 48 5 32.

Possible answer: The rectangle could be 10 units

long and 2 units wide, since 10 3 2 5 20.

Area 5 5 3 4, or 20 square units

Tent A’s floor has the greater area.

The area of the white space is 32 square units.

C

M

M

M

©Curriculum Associates, LLC Copying is not permitted. 321Lesson 30 Connect Area and Perimeter

Name:

Prerequisite: Multiply to Find Area

Study the example problem showing how to multiply to find the area of a rectangle. Then solve problems 1–7.

1 Show how to fi nd the area of rectangle A.

2 Write the multiplication sentence you would use to fi nd the area of rectangle B.

3 5

3 Mr. Taro’s deck is 5 meters long and 3 meters wide. He has enough stain to cover 18 square meters of wood. Does he have enough stain to cover the deck? Explain.

Example

Jared is planting grass in a section of his yard. The diagram shows the length and width of the section. What is the area of this part of Jared’s yard?

You know the length and width of the rectangle.

You multiply length by width to find the area of a rectangle.

7 yards 3 3 yards 5 21 square yards

Area 5 21 square yards

Connect Area and Perimeter

Lesson 30

3 yards

7 yards

6 m

A3 m

4 m

B7 m

321

Area 5 3 meters 3 6 meters 5 18 square meters

Possible answer: The area of the deck is

5 meters 3 3 meters, or 15 square meters.

Since he has enough stain to cover 18 square

meters, he has more than he needs.

4 7 28

M

B

B

126©

Cu

rriculu

m A

ssociates, LL

C

Copyin

g is not perm

itted.


eterU

nit 5

Practice and Prob

lem Solvin

gU

nit 5 Measurem

ent and D

ata


Solve.

4 Lorenzo knows that the perimeter of the trapezoid is 18 centimeters. Show how to fi nd the length of the top side. Write the length in the blank.

5 Nadia makes this sign for her bedroom door. She wants to put a ribbon border around all the edges of the sign. She has 12 inches of ribbon. Is this enough?

6 The perimeter of this shape is 20 feet. Show how to fi nd the missing side length.

7 Jeff has a garden in the shape of a hexagon. Each of the 6 sides of the hexagon is 6 feet long. What is the perimeter of the garden?

8 A rectangle has 2 sides that are each 6 centimeters long. The perimeter is 22 centimeters. How long are the other two sides?

Show your work.

Solution:

8 cm

cm

3 cm 3 cm

2 in.2 in.

5 in.

5 in.

N

3 ft

3 ft?

1 ft

3 ft

6 ft

324

3 1 8 1 3 5 14 and 18 2 14 5 4 centimeters

Possible answer: Nadia does not have enough

ribbon. The perimeter of the sign is 5 1 2 1 2 1

5 1 2 1 2, or 18 inches. 18 inches . 12 inches

Add the given lengths: 6 1 3 1 3 1 1 1 1 1 1 1 3 5 18.

Subtract the sum from the perimeter: 20 2 18 5 2.

The missing side length is 2 feet.

6 sides 3 6 feet each 5 36 feet;

perimeter 5 36 feet

Possible work: 6 1 6 5 12 and 22 2 12 5 10. So, the sum of the other two sides has to be 10 centimeters. 5 1 5 5 10

The other sides are 5 centimeters long.

4

C

M

M

M

M


Name: Lesson 30

Find the Missing Side Length

Study the example problem showing how to use perimeter to find the missing side length of a shape. Then solve problems 1–8.

1 Write an equation to fi nd the perimeter of this rectangle.

2 The perimeter of this triangle is 12 feet. How can you fi nd the missing side length? What is the length?

3 A square has a perimeter of 20 inches. Explain how to fi nd the length of each side.

Example

This is a floor plan of the shed that Sean is going to build. The perimeter of the shed is 16 meters. What is the missing side length?

The perimeter is 16 meters. That means that the sum of all the side lengths is 16.

5 1 3 1 3 1 2 1 1 1 ? 5 16

14 1 ? 5 16, so ? 5 2

The missing side length is 2 meters.

3 meters2 meters

?1 meter

5 meters

3 meters

Vocabularyperimeter the distance

around a shape; found

by finding the sum of the

side lengths.

4 m

4 m

3 m 3 m

?

5 ft3 ft

323

4 1 3 1 4 1 3 5 14; perimeter 5 14 meters

Possible answer: Add the side lengths that are given.

Then subtract the sum from the perimeter. 3 1 5 5 8

and 12 2 8 5 4. The missing side length is 4 feet.

Possible answer: All four sides of a square are

the same length. Divide the perimeter by 4 to

find the side length. 20 4 4 5 5. Each side is

5 inches long.

M

M

B

127©

Cu

rriculu

m A

ssociates, LL

C

Copyin

g is not perm

itted.


eterU

nit 5

Practice and Prob

lem Solvin

gU

nit 5 Measurem

ent and D

ata


Solve.

3 Simone has 16 square-inch tiles. She glues them on cardboard to make two diff erent rectangles, each with the same area. What are the lengths and widths of two rectangles she can make?

Show your work.

Solution:

4 Simone wants to glue colored string around the edges of the two rectangles she made. What is the total length of string she needs for each frame?

Show your work.

Solution:

5 Enrique drew the rectangle at the right. Draw another rectangle with the same area but diff erent side lengths. Which rectangle has the greater perimeter?

326

Possible work: 16 4 2 5 8, so the area of each rectangle is 8 square inches. 4 3 2 5 8 and 8 3 1 5 8

Possible work: 4 1 2 1 4 1 2 5 12 and 8 1 1 1 8 1 1 5 18

Possible answer: One rectangle has a length

of 4 inches and a width of 2 inches. The other rectangle

has a length of 8 inches and a width of 1 inch.

Possible answer: Simone needs 12 inches

of string for one rectangle and 18 inches of string

for the other rectangle.

Enrique’s rectangle has a perimeter of 18 units. My rectangle has a perimeter of

24 units. My rectangle has the greater perimeter.

Possible answer:

M

M

C


Name: Lesson 30

Same Area and Different Perimeter

Study the example showing how rectangles with the same area can have different perimeters. Then solve problems 1–5.

1 Both rectangles on the right have an area of 12 square units. Write the perimeter of each in the table.

Length Width Area Perimeter

12 units 1 unit12 square

units units

4 units 3 units12 square

units units

2 Draw two diff erent rectangles that have an area of 10 square units. Write the number of units for each length, width, and perimeter.

1: length 5 , width 5 , perimeter 5

2: length 5 , width 5 , perimeter 5

Example

Chang has 12 square tiles. He uses the tiles to make two different rectangles that each have an area of 6 square units. Do these rectangles have the same perimeter?

6 units3 units

3 units6 units

1 unit 1 unit 2 units 2 units

Rectangles with the same area can have different perimeters.




side lengths.

6 1 1 1 6 1 1 5 14 3 1 2 1 3 1 2 5 10perimeter 5 14 units perimeter 5 10 units

325

26

14

10 1 22

5 2 14

M

B

128©

Cu

rriculu

m A

ssociates, LL

C

Copyin

g is not perm

itted.


eterU

nit 5

Practice and Prob

lem Solvin

gU

nit 5 Measurem

ent and D

ata


Solve. Use Rectangles A, B, and C for problems 3–5.

3 Which rectangle has the greatest area?

Show your work.

Solution:

4 Which rectangles have the same perimeter?

Show your work.

Solution:

5 Draw a rectangle that has the same perimeter as Rectangle A. Use diff erent side lengths than the ones in Rectangles A, B, or C. Write the length, width, and area of your rectangle.

length

width

area

6 Find the lengths and widths of two diff erent rectangles that have a perimeter of 20 units. Then fi nd and compare their areas.

5 units

B5 units

4 units

C5 units

6 units

A3 units

328

Area of A: 3 3 6 5 18 square unitsArea of B: 5 3 5 5 25 square unitsArea of C: 5 3 4 5 20 square units

Perimeter of A: 3 1 6 1 3 1 6 5 18 unitsPerimeter of B: 5 1 5 1 5 1 5 5 20 unitsPerimeter of C: 5 1 4 1 5 1 5 5 18 units

7 units

14 square units

2 units

Rectangles A and C have the same perimeter.

Possible answer: A rectangle with sides of 6 units and 4 units has a perimeter of

20 units and an area of 24 square units. Another rectangle with sides of 7 units and

3 units has a perimeter of 20 units and an area of 21 square units.

The 6 unit 3 4 unit rectangle has a greater area.

Rectangle B has the greatest area.

Possible answer:

C

M

M

M


Name:

Same Perimeter and Different Area

Study the example showing that rectangles with the same perimeter can have different areas. Then solve problems 1–6.

1 Both rectangles on the right have a perimeter of 14 units. Write the area of each in the table.


6 units 1 unit square units

14 units

5 units 2 units square units

14 units

2 Draw a diff erent rectangle that has a perimeter of 14 units. Write the length, width, and area in the table.


units units square units14 units

Example

Kat drew two different rectangles, each with a perimeter of 10 units. Do these rectangles have the same area?

Rectangles with the same area can have different perimeters.

Lesson 30




side lengths.

length 5 4 units and width 5 1 unit length 5 3 units and width 5 2 units

area 5 4 square units area 5 6 square units

327

6

10

Possible answer:

4 3 12

C

B

129©

Cu

rriculu

m A

ssociates, LL

C

Copyin

g is not perm

itted.


eterU

nit 5

Practice and Prob

lem Solvin

gU

nit 5 Measurem

ent and D

ata


6 Draw a rectangle that has the same area but a diff erent perimeter than the rectangle in problem 4. Find the perimeter and area of your new rectangle.

Perimeter:

Area:

Solve.

4 Find the perimeter and area of the rectangle.

Perimeter:

Area:

5 Draw a rectangle that has the same perimeter but a diff erent area than the rectangle in problem 4. Find the perimeter and area of your new rectangle.

Perimeter:

Area:

You might start by labeling the length of each side in units.

Try making the length or width 1 unit less or more.

What are some other numbers you can multiply to get the number you found for the area in problem 4?

330

22 units

22 units

26 units

30 square units

28 square units

30 square units

M

C

B

Possible answer:

Possible answer:


Name:

3 Find the perimeter and area of this rectangle.

Show your work.

Solution:

2 For which of the following would you fi nd the perimeter? Circle the letter for all that apply.

A the amount of space on a wall to paint

B the amount of fencing needed to go around a yard

C the length of wood needed to frame a picture

D the amount of space a tablecloth covers

1 A rectangular rug is 10 feet long and 7 feet wide. What is the perimeter of the rug? Circle the letter of the correct answer.

A 17 feet C 68 feet

B 34 feet D 70 feet

Ami chose D as the correct answer. How did she get that answer?

Connect Area and Perimeter

Solve the problems.

Lesson 30

What measurement does the problem ask you to find?

Remember, perimeter is the distance around a shape.

There are different ways to break the shape into rectangles.

329

Possible answer: Ami multiplied the length of the

rug by the width. That’s how you find the area. She

should have added the lengths of all four sides.

perimeter 5 18 units, area = 16 square units

M

M

M

Possible student work:2 1 2 1 1 1 4 1 3 1 6 5 182 3 2 1 3 3 4 5 16

practice lesson 30 connect area and perimeter b m€¦ · practice lesson 30 connect area and...

Documents