Question 1: Calculate the area of a shape composed of a rectangle (6 cm by 4 cm) and a square (3 cm by 3 cm) joined together. Use breaking down to find the total area.

Answer: 39

Question 2: Decompose a L-shaped figure (dimensions: 8 cm by 3 cm and 5 cm by 3 cm, arranged to form an L). Calculate its total area by splitting it into two rectangles.

Answer: 39

Question 3: A composite shape consists of a rectangle (10 cm by 4 cm) with a semicircular extension of radius 2 cm on one side. Break down the shape and find the total area.

Answer: 54.57

Question 4: Construct a triangle with a base of 6 cm and height of 5 cm, then add a rectangle of 4 cm by 3 cm adjacent to it. Find the total area by breaking down the shape.

Answer: 48

Question 5: A compound shape is made up of two rectangles: one 7 cm by 3 cm and another 5 cm by 2 cm, placed side by side. Calculate the combined area using breaking down.

Answer: 29

Question 6: A shape consists of a rectangle (9 cm by 4 cm) and a triangle on top with a base of 9 cm and height of 3 cm. Find the total area by breaking down into parts.

Answer: 45.5

Question 7: A floor plan shows a kitchen area made of two parts: a rectangular section (6 m by 4 m) and an adjacent rectangular extension (3 m by 4 m). Calculate the total area.

Answer: 36

Question 8: A park is designed as a large rectangle (50 m by 20 m) with a semicircular playground of radius 5 m in one corner. Break down the shapes and find the total area.

Answer: 1132.7

Question 9: Problem-solving: Decompose a complex shape made of a rectangle (12 cm by 5 cm) and a right-angled triangle (base 3 cm, height 5 cm) attached on one side. Calculate total area.

Answer: 87

Question 10: Identify and correct the mistake in the following calculation: A shape is split into two rectangles (4 cm by 3 cm and 2 cm by 3 cm). The total area is given as 18 cm², but the student calculated 24 cm².

Answer: Incorrect; the correct total area is 18 cm², calculated as 4×3 + 2×3 = 12 + 6 = 18.

Question 11: Challenge: Break down and find the area of a complex shape made up of a rectangle (10 cm by 6 cm), a square (4 cm by 4 cm), and a right-angled triangle (base 4 cm, height 3 cm) joined together.

Answer: 106