Question 1: Calculate the perimeter of a rectangle measuring 8 cm by 5 cm.

Answer: 26

Question 2: A L-shaped figure is formed by a rectangle of 10 cm by 4 cm and a square of 4 cm by 4 cm attached to it. Break down the figure and find its perimeter.

Answer: 36

Question 3: Construct a shape on the grid with two rectangles sharing a side, with total perimeter 24 cm. One rectangle is 6 cm by 4 cm, the other is 5 cm by 3 cm. Show your steps.

Answer: Perimeter = 6+4+6+4 + 5+3+5+3 = 24

Question 4: Explain how breaking down a compound shape into simpler rectangles helps in calculating perimeter.

Answer: Breaking down allows calculation of individual perimeters and summing, avoiding double counting shared sides.

Question 5: A shape consists of a rectangle (7 cm by 3 cm) with a square (3 cm by 3 cm) attached on top. Break down and find the perimeter.

Answer: Perimeter = 7+3+7+3 + 3+3 (top side) + 3 (attached square side) = 26

Question 6: Plot the graph of y = 2x for x from 0 to 5. Use this to help estimate the perimeter of a shape formed by connecting points at (0,0), (2,4), (4,8), (5,10).

Answer: Segments: (0,0)-(2,4): 4.47; (2,4)-(4,8): 4.47; (4,8)-(5,10): 2.24; total approximately 11.18 cm

Question 7: A compound shape has three rectangles: 6 cm by 4 cm, 4 cm by 3 cm, and 5 cm by 2 cm, arranged in a row. Break down and find the total perimeter of the combined shape.

Answer: Total perimeter = 6+4+6+4+5+2+5+2 minus shared sides, resulting in 24 cm

Question 8: A shape is made by combining a rectangle (9 cm by 4 cm) and a triangle with base 4 cm and height 3 cm. Break down the perimeter.

Answer: Calculate triangle sides using Pythagoras, then sum all outer sides: 9+4+ (triangle sides) + base = total perimeter

Question 9: Identify a common mistake when breaking down shapes for perimeter calculation and suggest how to correct it.

Answer: Mistake: Double counting shared sides. Correct by subtracting lengths of shared edges or carefully counting only outer sides.

Question 10: Find the perimeter of an irregular shape composed of rectangles of 5 cm by 3 cm, 2 cm by 2 cm, and 4 cm by 3 cm, arranged in a 'U' shape. Show your method.

Answer: Sum all outer sides after breaking down and removing double-counted shared sides; approximate perimeter around 22 cm