## Engage NY Eureka Math 3rd Grade Module 4 Lesson 11 Answer Key

### Eureka Math Grade 3 Module 4 Lesson 11 Problem Set Answer Key

Question 1.

The rectangles below have the same area. Move the parentheses to find the unknown side lengths. Then, solve.

a.

Area: 8 × __6____ = __48____

Area: ___48___ sq cm

Answer:

The area of the rectangle = 48 sq cm.

Explanation:

In the above-given question,

given that,

The area of the rectangle = l x b.

where l = length, b = breadth.

area = 6 x 8 = 48.

area of the rectangle = 48 sq cm.

b.

Area: 1 × 48 = __( 1_x_6)_x 8

Area: __48____ sq cm

Answer:

The area of the rectangle = 48 sq cm.

Explanation:

In the above-given question,

given that,

The area of the rectangle = l x b.

where l = length, b = breadth.

area = 48 x 1 = 48.

area of the rectangle = 48 sq cm.

c.

Area: 8 × 6 = (2 × 4) × 6

= 2 × 4 × 6

= __8____ × __6____

= __48____

Area: __48____ sq cm

Answer:

The area of the rectangle = 48 sq cm.

Explanation:

In the above-given question,

given that,

The area of the rectangle = l x b.

where l = length, b = breadth.

area = 8 x 6 = 48.

area = 8 x 6 = (2 x 4) x 6.

2 x ( 4 x 6).

2 x 24.

area of the rectangle = 48 sq cm.

d.

Area: 8 × 6 = (4 × 2) × 6

= 4 × 2 × 6

= ___4___ × ___12___

= __48____

Area: ___48___ sq cm

Answer:

The area of the rectangle = 48 sq cm.

Explanation:

In the above-given question,

given that,

The area of the rectangle = l x b.

where l = length, b = breadth.

area = 8 x 6 = 48.

area = 8 x 6 = (4 x 2) x 6.

area = 4 x 12.

area of the rectangle = 48 sq cm.

e.

Area: 8 × 6 = 8 × (2 × 3)

= 8 × 2 × 3

= __16____ × ___3__

= ___48___

Area: ___48___ sq cm

Answer:

The area of the rectangle = 48 sq cm.

Explanation:

In the above-given question,

given that,

The area of the rectangle = l x b.

where l = length, b = breadth.

area = 8 x 6 = 48.

area = 8 x 6 = (8 x 2) x 3.

area = 16 x 3.

area of the rectangle = 48 sq cm.

Question 2.

Does Problem 1 show all the possible whole number side lengths for a rectangle with an area of 48 square centimeters? How do you know?

Answer:

The area of the rectangle = 48 sq cm.

Explanation:

In the above-given question,

given that,

The area of the rectangle = l x b.

where l = length, b = breadth.

area = 8 x 6 = 48.

area = 8 x 6 = (4 x 2) x 6.

area = 4 x 12.

area of the rectangle = 48 sq cm.

Question 3.

In Problem 1, what happens to the shape of the rectangle as the difference between the side lengths gets smaller?

Answer:

The area of the rectangle also decreases= 48 sq cm.

Explanation:

In the above-given question,

given that,

The area of the rectangle = l x b.

where l = length, b = breadth.

area = 8 x 6 = 48.

area = 8 x 6 = (4 x 2) x 6.

area = 4 x 12.

area of the rectangle = 48 sq cm.

Question 4.

a. Find the area of the rectangle below.

Answer:

The area of the rectangle = 72 sq cm.

Explanation:

In the above-given question,

given that,

area of the rectangle = l x b.

where l = length, b = breadth.

l = 8 cm and b = 9 cm given.

area = l x b.

area = 8 x 9.

area = 72 sq cm.

b. Julius says a 4 cm by 18 cm rectangle has the same area as the rectangle in Part (a). Place parentheses in the equation to find the related fact and solve. Is Julius correct? Why or why not?

4 × 18 = 4 × 2 × 9

= 4 × 2 × 9

= ___8___ × __9____

= __72____

Area: __72___ sq cm

Answer:

Yes, Julius was correct.

Explanation:

In the above-given question,

given that,

The area of the rectangle = l x b.

where l = length, b = breadth.

area = 4 x 18 = 72.

area = 4 x 18 = (4 x 2) x 9.

area = 8 x 9.

area of the rectangle = 72 sq cm.

c. Use the expression 8 × 9 to find different side lengths for a rectangle that has the same area as the rectangle in Part (a). Show your equations using parentheses. Then, estimate to draw the rectangle and label the side lengths.

Answer:

The area of the rectangle = 72 sq cm.

Explanation:

In the above-given question,

given that,

The area of the rectangle = l x b.

where l = length, b = breadth.

area = 8 x 9 = 72.

area = 8 x 9 = (4 x 2) x 9.

area = 4 x 18.

area of the rectangle = 72 sq cm.

### Eureka Math Grade 3 Module 4 Lesson 11 Exit Ticket Answer Key

Question 1.

Find the area of the rectangle.

Answer:

The area of the rectangle = 64 sq cm.

Explanation:

In the above-given question,

given that,

The area of the rectangle = l x b.

where l = length, b = breadth.

area = 8 x 8 = 64.

area = 8 x 8 = (4 x 2) x 8.

area = 4 x 16.

area of the rectangle = 64 sq cm.

Question 2.

The rectangle below has the same area as the rectangle in Problem 1. Move the parentheses to find the unknown side lengths. Then, solve.

Area: 8 × 8 = (4 × 2) × 8

= 4 × 2 × 8

= __8____ × __8____

= __64____

Area: __64____ sq cm

Answer:

The area of the rectangle = 64 sq cm.

Explanation:

In the above-given question,

given that,

The area of the rectangle = l x b.

where l = length, b = breadth.

area = 8 x 8 = 64.

area = 8 x 8 = (4 x 2) x 8.

area = 4 x 16.

area of the rectangle = 64 sq cm.

### Eureka Math Grade 3 Module 4 Lesson 11 Homework Answer Key

Question 1.

The rectangles below have the same area. Move the parentheses to find the unknown side lengths.

Then, solve.

a.

Area: 4 × ___9___ = ___36___

Area: __36____ sq cm

Answer:

The area of the rectangle = 36 sq cm.

Explanation:

In the above-given question,

given that,

The area of the rectangle = l x b.

where l = length, b = breadth.

area = 4 x 9 = 36.

area = 4 x 9 = (4 x 3) x 3.

area = 4 x 9.

area of the rectangle = 36 sq cm.

b.

Area: 1 × 36 = __36____

Area: ___36___ sq cm

Answer:

The area of the rectangle = 36 sq cm.

Explanation:

In the above-given question,

given that,

The area of the rectangle = l x b.

where l = length, b = breadth.

area = 1 x 36 = 36.

area = 1 x 36 = (1 x 6) x 6.

area = 6 x 6.

area of the rectangle = 36 sq cm.

c.

Area: 4 × 9 = (2 × 2) × 9

= 2 × 2 × 9

= __4____ × __9____

= ___36___

Area: __36____ sq cm

Answer:

The area of the rectangle = 36 sq cm.

Explanation:

In the above-given question,

given that,

The area of the rectangle = l x b.

where l = length, b = breadth.

area = 4 x 9 = 36.

area = 4 x 9 = (4 x 3) x 3.

area = 12 x 3.

area of the rectangle = 36 sq cm.

d.

Area: 4 × 9 = 4 × (3 × 3)

= 4 × 3 × 3

= ___12___ × __3____

= ___36___

Area: ___36___ sq cm

Answer:

The area of the rectangle = 36 sq cm.

Explanation:

In the above-given question,

given that,

The area of the rectangle = l x b.

where l = length, b = breadth.

area = 4 x 9 = 36.

area = 4 x 9 = (4 x 3) x 3.

area = 12 x 3.

area of the rectangle = 36 sq cm.

e.

Area: 12 × 3 = (6 × 2) × 3

= 6 × 2 × 3

= ___6___ × __6____

= __36____

Area: ___36___ sq cm

Answer:

The area of the rectangle = 36 sq cm.

Explanation:

In the above-given question,

given that,

The area of the rectangle = l x b.

where l = length, b = breadth.

area = 12 x 3 = 48.

area = 12 x 3 = (6 x 2) x 3.

area = 12 x 3.

area of the rectangle = 36 sq cm.

Question 2.

Does Problem 1 show all the possible whole number side lengths for a rectangle with an area of 36 square centimeters? How do you know?

Answer:

The area of the rectangle = 36 sq cm.

Explanation:

In the above-given question,

given that,

The area of the rectangle = l x b.

where l = length, b = breadth.

area = 6 x 6 = 36.

area = 6 x 6 = (6 x 2) x 3.

area = 12 x 3.

area of the rectangle = 36 sq cm.

Question 3.

a. Find the area of the rectangle below.

Answer:

The area of the rectangle = 48 sq cm.

Explanation:

In the above-given question,

given that,

The area of the rectangle = l x b.

where l = length, b = breadth.

area = 6 x 8 = 48.

area of the rectangle = 48 sq cm.

b. Hilda says a 4 cm by 12 cm rectangle has the same area as the rectangle in Part (a). Place parentheses in the equation to find the related fact and solve. Is Hilda correct? Why or why not?

4 × 12 = 4 × 2 × 6

= 4 × 2 × 6

= __8____ × __6____

= ___48___

Area: __48____ sq cm

Answer:

The area of the rectangle = 48 sq cm.

Explanation:

In the above-given question,

given that,

The area of the rectangle = l x b.

where l = length, b = breadth.

area = 4 x 12 = 48.

area = 4 x 12 = (4 x 2) x 6.

area = 8 x 6.

area of the rectangle = 48 sq cm.

c. Use the expression 8 × 6 to find different side lengths for a rectangle that has the same area as the rectangle in Part (a). Show your equations using parentheses. Then, estimate to draw the rectangle and label the side lengths.

Answer:

The area of the rectangle = 48 sq cm.

Explanation:

In the above-given question,

given that,

The area of the rectangle = l x b.

where l = length, b = breadth.

area = 4 x 12 = 48.

area = 4 x 12 = (4 x 2) x 6.

area = 8 x 6.

area of the rectangle = 48 sq cm.