Same area, different perimeter (and the other way round)

Question 1

Rectangle A is 3 cm by 8 cm. Rectangle B is 4 cm by 6 cm. They have the same area. Which has the greater perimeter?

• A. Rectangle A
• B. Rectangle B

Question 2

Leo says: "If two rectangles have the same area, they must have the same perimeter." True or false? (Think about 3 × 4 and 12 × 1.)

• A. true
• B. false

Question 3

Two rectangles both have a perimeter of 20 cm. One is 4 cm by 6 cm, the other is 5 cm by 5 cm. What is the difference between their areas, in cm²?

Answer 

Question 4

Rectangle A is 5 cm by 6 cm. Rectangle B is 2 cm by 15 cm. They have the same area. Which has the greater perimeter?

• A. Rectangle A
• B. Rectangle B

Question 5

Arjun says: "If two rectangles have the same area, they must have the same perimeter." True or false? (Think about 4 × 4 and 16 × 1.)

• A. true
• B. false

Question 6

Two rectangles both have a perimeter of 24 cm. One is 1 cm by 11 cm, the other is 6 cm by 6 cm. What is the difference between their areas, in cm²?

Answer 

Question 7

Rectangle A is 4 cm by 4 cm. Rectangle B is 1 cm by 16 cm. They have the same area. Which has the greater perimeter?

• A. Rectangle A
• B. Rectangle B

Question 8

Zara says: "If two rectangles have the same area, they must have the same perimeter." True or false? (Think about 2 × 6 and 12 × 1.)

• A. true
• B. false

Question 9

Two rectangles both have a perimeter of 12 cm. One is 1 cm by 5 cm, the other is 3 cm by 3 cm. What is the difference between their areas, in cm²?

Answer 

Question 10

Rectangle A is 3 cm by 10 cm. Rectangle B is 5 cm by 6 cm. They have the same area. Which has the greater perimeter?

• A. Rectangle A
• B. Rectangle B

Question 11

Chloe says: "If two rectangles have the same area, they must have the same perimeter." True or false? (Think about 2 × 6 and 12 × 1.)

• A. true
• B. false

Question 12

Two rectangles both have a perimeter of 24 cm. One is 5 cm by 7 cm, the other is 6 cm by 6 cm. What is the difference between their areas, in cm²?

Answer 

Question 13

Rectangle A is 2 cm by 9 cm. Rectangle B is 3 cm by 6 cm. They have the same area. Which has the greater perimeter?

• A. Rectangle A
• B. Rectangle B

Question 14

Ravi says: "If two rectangles have the same area, they must have the same perimeter." True or false? (Think about 2 × 6 and 12 × 1.)

• A. true
• B. false

Question 15

Two rectangles both have a perimeter of 24 cm. One is 2 cm by 10 cm, the other is 6 cm by 6 cm. What is the difference between their areas, in cm²?

Answer 

Question 16

Rectangle A is 2 cm by 6 cm. Rectangle B is 3 cm by 4 cm. They have the same area. Which has the greater perimeter?

• A. Rectangle A
• B. Rectangle B