Question 1: Calculate the perimeter of a shape made by combining a rectangle 8 cm by 5 cm and a square with side 5 cm, sharing the side of length 5 cm.

Answer: 23

Question 2: A compound shape consists of a rectangle 10 cm by 4 cm and a triangle attached to one of its longer sides. The triangle has a base of 6 cm and height 4 cm. Calculate the total perimeter if the triangle's other two sides are 5 cm and 7 cm.

Answer: 36

Question 3: Construct a shape on the grid that is a rectangle 6 cm by 3 cm with a right-angled triangle 3 cm by 4 cm attached to one side. Find the perimeter of the combined shape.

Answer: 22

Question 4: A L-shaped figure is formed by two rectangles, one 10 cm by 4 cm and the other 6 cm by 4 cm, joined along a 4 cm side. Calculate the perimeter of the L-shape.

Answer: 28

Question 5: Explain how breaking down a complex shape into rectangles can simplify perimeter calculation. Provide a brief example.

Answer: By dividing the shape into rectangles, each side can be measured and added separately, then combined to find total perimeter, e.g., an L-shape can be split into two rectangles, perimeter found separately, then summed.

Question 6: A shape is made by combining a 12 cm by 5 cm rectangle and a 5 cm by 3 cm rectangle sharing a 5 cm side. Calculate the total perimeter of the shape.

Answer: 28

Question 7: A garden layout consists of a large rectangular pond 15 m by 10 m with a walkway 2 m wide surrounding it. Construct the outer boundary shape and calculate its perimeter.

Answer: 94

Question 8: A complex shape can be broken down into three rectangles: 8 cm by 3 cm, 6 cm by 4 cm, and 4 cm by 3 cm. If they are arranged to form a larger shape, find its perimeter.

Answer: 34

Question 9: Identify a common mistake when calculating the perimeter of a compound shape by simply adding all sides without considering shared sides. How can this mistake be avoided?

Answer: Adding all sides without accounting for shared sides leads to overestimation. To avoid this, subtract the lengths of shared sides that are counted twice.

Question 10: A shape consists of a rectangle 9 cm by 4 cm with a semicircular extension of diameter 4 cm attached to one side. Calculate the perimeter of the shape, including the curved part.

Answer: 36.57

Question 11: Challenge: Design a composite shape on the grid that includes at least two rectangles and a triangle. Find the perimeter of the entire shape after breaking it down into simpler parts.

Answer: Variable depending on design, but expect around 40-50

Question 12: Error Analysis: A student calculated the perimeter of a shape by adding the lengths of all sides, including those that are shared between shapes. Identify the mistake and suggest the correct approach.

Answer: The mistake is double-counting shared sides. The correct approach is to add only the outer sides after breaking down the shape or subtract shared sides once.