## 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

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

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

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

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

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?

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?

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.

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

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.

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.

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

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

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

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

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

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

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?

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.

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

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.