Question 1: Calculate the area of the shaded region by subtracting the smaller rectangle's area from the larger one.

Answer: 24

Question 2: A compound shape has a total area of 60 cm². If a cut removes an area of 15 cm², what is the remaining area?

Answer: 45

Question 3: A rectangle measures 12 cm by 8 cm. A smaller rectangle of 3 cm by 4 cm is cut out from its corner. What is the remaining area?

Answer: 84

Question 4: Identify the mistake in the following subtraction: A shape has an area of 50 cm². A section of 20 cm² is removed, but the answer given was 40 cm².

Answer: Incorrect subtraction; 50 - 20 = 30, not 40.

Question 5: A garden layout is a large rectangle of 30 m by 20 m. A pond of 10 m by 4 m is to be added, but the area of the pond is subtracted for planting. What area remains for planting after subtracting the pond's area?

Answer: 560

Question 6: Construct a rectangle with a length of 15 cm and a width of 10 cm. Then, subtract a smaller rectangle of 5 cm by 4 cm from one corner. What is the remaining area?

Answer: 130

Question 7: A composite shape has an area of 48 cm², and a cutout of 18 cm² is removed. What is the area of the remaining shape?

Answer: 30

Question 8: Explain why subtracting the area of a smaller shape from a larger one might lead to an error if the shapes overlap or share a boundary.

Answer: Overlap or shared boundary can cause double counting or incorrect subtraction, so careful analysis is needed.

Question 9: The area of a large rectangle is 100 cm². A smaller rectangle of 30 cm² is subtracted. Which of the following is the correct remaining area? (a) 70 cm² (b) 80 cm² (c) 60 cm².

Answer: a

Question 10: A shape has an area of 72 cm². If a section of 25 cm² is removed, but the student mistakenly subtracts 20 cm², what is the student's answer and what is the correct area?

Answer: Student's answer: 52; Correct answer: 47

Question 11: Challenge: A compound L-shaped figure has an area of 80 cm². If a rectangular section of 20 cm² is removed incorrectly by subtracting 25 cm², what is the true remaining area?

Answer: 60