Question 1: Calculate the area of a rectangle measuring 8 cm by 3 cm.

Answer: 24

Question 2: A compound shape consists of a rectangle (6 cm by 4 cm) and a right-angled triangle with a base of 3 cm and height of 4 cm. Find the total area.

Answer: 36

Question 3: A L-shaped figure is made by combining two rectangles: one 10 cm by 4 cm and the other 6 cm by 4 cm. Calculate its total area.

Answer: 64

Question 4: Construct a shape on the grid that is made of two rectangles with areas 12 cm² and 8 cm². Calculate the total area.

Answer: 20

Question 1: A composite shape is made of a rectangle 10 cm by 6 cm and a triangle on top with a base of 10 cm and height of 4 cm. Explain how to find the total area and calculate it.

Answer: Total area = area of rectangle + area of triangle = (10×6) + (1/2×10×4) = 60 + 20 = 80 cm²

Question 2: A shape is composed of a 5 cm by 5 cm square and a right-angled triangle with a base of 5 cm and height of 3 cm attached to one side. Find the total area and explain each step.

Answer: Area of square = 25; area of triangle = 1/2×5×3=7.5; total = 25+7.5=32.5 cm²

Question 3: A shape consists of two overlapping rectangles, one 8 cm by 3 cm and the other 6 cm by 4 cm, overlapping such that the overlapping area is 4 cm². Find the total area of the combined shape.

Answer: 20

Question 1: A garden is designed in the shape of a large rectangle (12 m by 8 m) with a semi-circular pond (radius 2 m) in one corner. Find the total planting area outside the pond.

Answer: Area of rectangle = 96; area of semi-circle = 1/2×π×2²=2π≈6.28; total = 96-6.28≈89.72 m²

Question 2: A floor plan shows a room made of a rectangle 9 m by 5 m and a corridor attached with dimensions 4 m by 1.5 m. Calculate the total floor area.

Answer: Total area = 45 + 6 = 51 m²

Question 1: A compound shape consists of a rectangle 10 cm by 7 cm and a right-angled triangle with a base of 4 cm and a height of 7 cm. The triangle is attached to the top of the rectangle. Find the total area, explaining each step.

Answer: Rectangle area = 70; triangle area = 1/2×4×7=14; total = 70+14=84 cm²

Question 2: A L-shaped figure is formed by three rectangles with dimensions 4×3, 5×2, and 3×2. The overlapping parts are accounted for to avoid double counting. Calculate the total area, showing your breakdown.

Answer: Total = (12+10+6) - overlaps; overlaps are carefully subtracted; final answer = 22

Question 1: A student calculates the area of a compound shape by adding the areas of its parts without checking overlaps or gaps. Explain why this may lead to an incorrect answer and how to fix it.

Answer: Adding without considering overlaps can double count or miss parts; fix by subtracting overlaps or rechecking boundaries.

Question 2: A student computes the area of a shape made of a rectangle 8 cm by 5 cm and a triangle with base 8 cm and height 3 cm. Instead of summing, they subtract the triangle's area. Is this correct? Explain.

Answer: No, the triangle is part of the shape; total area should be sum, not difference.