Question 1: Calculate the area of the shaded region when a rectangle of length 12 m and width 8 m has a rectangular cutout of length 5 m and width 3 m removed.

Answer: 69

Question 2: A circular patio of radius 7 m has a semicircular garden attached, with radius 4 m. Find the total combined area of the patio and garden, subtracting the garden from the patio area if they overlap partially.

Answer: 227.25

Question 3: A building plan shows a main hall measuring 20 m by 15 m, with an L-shaped storage room measuring 6 m by 4 m attached. Calculate the remaining area of the main hall after subtracting the storage room area.

Answer: 204

Question 4: A rectangular garden measures 18 m in length and 10 m in width. A pathway of width 2 m runs around the inside edge of the garden, reducing planting space. Calculate the area of the remaining planting zone.

Answer: 176

Question 5: A designer plans a custom window frame that is 3 m high and 2.5 m wide. The inner glass pane measures 2.8 m by 2.2 m. Find the area of the frame material, subtracting the glass area from the total frame area.

Answer: 4.35

Question 6: A wall in an architectural model is 30 cm long and 10 cm high. A doorway of 3 cm by 2.5 cm is cut out. Calculate the area of the remaining wall, showing your working.

Answer: 285

Question 7: A floor plan includes a main rectangular room measuring 25 m by 12 m. An adjacent L-shaped extension measures 8 m by 6 m and 4 m by 4 m. Calculate the total floor area after subtracting the extension area from the main room, assuming they are connected.

Answer: 324

Question 8: A landscape designer needs to subtract a pond measuring 10 m by 6 m from a garden space of 40 m by 25 m. What is the remaining garden area?

Answer: 950

Question 9: Construct a rectangle with an area of 48 m², then subtract a square of side 4 m from it. Find the remaining area.

Answer: 32

Question 10: A large conference hall is 50 m long and 30 m wide. A stage measuring 10 m by 8 m is set up at one end. Calculate the area of the hall excluding the stage.

Answer: 1424

Question 11: A building rooftop has a rectangular area of 60 m by 20 m. A helicopter landing pad measuring 15 m by 15 m is placed on it. Calculate the remaining free space on the rooftop.

Answer: 1050

Question 12: Common mistake: A student calculates the area of a rectangle 10 m by 5 m as 50 m², then subtracts a square of side 3 m (area 9 m²) and gets 41 m² as the remaining area. Identify and correct the mistake.

Answer: Correct remaining area is 41 m²; the calculation is correct. The mistake is assuming the areas are simply subtractable without considering the shared boundaries or shape irregularities.