## Engage NY Eureka Math 5th Grade Module 5 Lesson 12 Answer Key

### Eureka Math Grade 5 Module 5 Lesson 12 Problem Set Answer Key

Question 1.

Measure each rectangle to the nearest \(\frac{1}{4}\) inch with your ruler, and label the dimensions. Use the area model to find each area.

Answer:

a.

Area =

2 x 2 = 4 sq. in.

1 x 1 = 1 sq. in.

Total = 4 + 1 = 5 square inches

b.

Area =

1 + 3/4 + 3/4 + 9/16

= 1 + 12/16 + 12/16 + 9/16

= 3 1/6 square inches.

c.

Area =

4 + 6/4

= 4 + 3/2

= 5 1/2 square inches

d.

Area =

6 + 3/4 + 3/4 + 116

=7 5/16 square inches

e.

Area = 6/4 + 3/8

= 12/8 + 3/8

= 1 7/8 square inches

f.

Area =

3/2 + 3/8

= 12/8 + 3/8

= 15/8

= 1 7/8 square inches

Question 2.

Find the area of rectangles with the following dimensions. Explain your thinking using the area model.

a. 1 ft × 1\(\frac{1}{2}\) ft

b. 1\(\frac{1}{2}\) yd × 1\(\frac{1}{2}\) yd

c. 2\(\frac{1}{2}\) yd × 1\(\frac{1}{16}\) yd

Answer:

a.

1 ft x 1 1/2 feet

= 1 1/2 square feet

b.

1 3/2 yd x 1 1/2 yd

= 1 + 1/2 +1/2 +1/4

= 1 + 2/4 + 2/4 +1/4

= 1 + 5/4

= 2 1/4 square yards

c.

2 1/2 yards x 1 3/16

= 2 + 1/2 + 6/16 + 3/32

= 2 + 16/32 + 12/32 + 3/32

= 2 + 31/32

= 2 31/32 square yards

Question 3.

Hanley is putting carpet in her house. She wants to carpet her living room, which measures 15 ft × 12\(\frac{1}{3}\) ft. She also wants to carpet her dining room, which is 10\(\frac{1}{4}\) ft × 10\(\frac{1}{3}\) ft. How many square feet of carpet will she need to cover both rooms?

Answer:

The area of the living room :

15 x 12 1/3

= 180 15/3

= 185 square feet

The area of the dining room =

10 1/4 x 10 1/3

= 41/4 x 31/3

= 1271/12

= 105 11/12 square feet

Total area = 185 + 105 11/12

= 290 11/12 square feet

Therefore, Hanley need 290 11/12 square feet of carpet to cover both the rooms.

Question 4.

Fred cut a 9\(\frac{3}{4}\)-inch square of construction paper for an art project. He cut a square from the edge of the big rectangle whose sides measured 3\(\frac{1}{4}\) inches. (See the picture below.)

a. What is the area of the smaller square that Fred cut out?

b. What is the area of the remaining paper?

Answer:

a.

Area = length x width

A = 3 1/4 x 3 1/4

= 13/4 x 13/4

= 169/16

= 10 9/16

Therefore, the area of the smaller square that fed cut out = 10 9/16

b.

Area of the large square =

9 3/4 x 9 3/4

= 39/4 x 39/4

= 1521/16

= 95 1/16

Now, 95 1/6 – 10 9/6 = 84 1/2 square inches

Therefore, The area of the remaining paper = 84 1/2 square inches.

### Eureka Math Grade 5 Module 5 Lesson 12 Exit Ticket Answer Key

Measure the rectangle to the nearest \(\frac{1}{4}\) inch with your ruler, and label the dimensions. Find the area.

Answer:

The dimensions of the rectangle =

2 1/4 inches and 1 1/2 inches

Area = length x width

= 2 1/4 x 1 1/2

= ( 2 x 1 ) + ( 2 x 1/2) + ( 1 x 1/4 ) + ( 1/4 x 1/2 )

= 2 + 1 + 1/4 + 1/8

= 27/8

= 3 3/8 square inches

### Eureka Math Grade 5 Module 5 Lesson 12 Homework Answer Key

Question 1.

Measure each rectangle to the nearest \(\frac{1}{4}\) inch with your ruler, and label the dimensions. Use the area model to find the area.

Answer:

a.

Area =

1 3/4 x 3 1/2

= 3 + 2 1/4 + 1/2 + 3/8

= 3 + 2 2/8 + 4/8 + 3/8

= 6 1/8 square inches

b.

Area =

3/4 x 2 1/4

= 1 1/2 + 3 /16

= 18/16 + 3/16

= 1 11/16 square inches

c.

Area =

2 1/4 x 2 1/4

= 4 + 2/4 + 2/4 + 1/16

= 5 1/16 square inches

d.

Area = 1 1/2 x 2 3/4

= 2 + 1 + 3/4 + 3/8

= 3 + 6/8 + 3/8

= 4 1/8 square inches

e.

Area =

1/2 x 1 3/4

=1/2 +3/8

= 7/8 square inches

Question 2.

Find the area of rectangles with the following dimensions. Explain your thinking using the area model.

a. 2\(\frac{1}{4}\) yd × \(\frac{1}{4}\) yd

b. 2\(\frac{1}{2}\) ft × 1\(\frac{1}{4}\) ft

Answer:

a.

2 1/4 x 1/4

= 2/4 +1/16

= 9/16 square yards

b.

2 1/2 ft x 1 1/4 ft

= 2 + 2/4 + 1/2 + 1/8

= 3 1/8 square feet

Question 3.

Kelly buys a tarp to cover the area under her tent. The tent is 4 feet wide and has an area of 31 square feet. The tarp she bought is 5\(\frac{1}{3}\) feet by 5\(\frac{3}{4}\) feet. Can the tarp cover the area under Kelly’s tent? Draw a model to show your thinking.

Answer:

Given, the measurements of tent =

Area = 31 square feet and 4 feet wide

Now, its length =31/7

=7 3/4 feet

The measurements of tarp she bought =

5 1/3 feet by 5 3/4 feet

= 25 + 15/4 + 5/3 + 3/12

= 25 + 3 3/4+ 1 2/3 + 1/4

= 30 2/3 square feet

Therefore, the tarp cannot cover the area under the tent.

Question 4.

Shannon and Leslie want to carpet a 16\(\frac{1}{2}\)-ft by 16\(\frac{1}{2}\)-ft square room. They cannot put carpet under an entertainment system that juts out. (See the drawing below.)

a. In square feet, what is the area of the space with no carpet?

b. How many square feet of carpet will Shannon and Leslie need to buy?

Answer:

a.

The area of the space with no carpet =

2 1/2 x 2 1/2

= 4 + 2/2+2/2 + 1/4

= 6 1/4

Therefore, the area of the space with no carpet = 6 1/4 square feet

b.

The measurements of the room as given =

16 1/2 x 16 1/2

= 256 + 16/2 + 16/2 + 1/4

= 256 + 8 + 8+ 1/4

= 256 + 16 + 1/4

= 272 1/4

We know that, the area of space with no carpet = 6 1/4

Now, 272 1/4 – 6 1/4

= 266 square feet

Therefore, Shannon and Leslie need to buy 266 square feet of carpet.