I'll solve this step by step, calculating the perimeter and area for both rooms A and B.
Room A:
Let me trace around the outside to find the perimeter:
- Top edge: 3 m
- Right side: 5 m
- Bottom right: 2 m (going left)
- Bottom middle vertical: 2 m (going down)
- Bottom left horizontal: 2 m (going left)
- Left side: 3 m (going up)
Perimeter = 3 + 5 + 2 + 2 + 2 + 3 = 17 m
For the area, I'll split it into two rectangles:
- Rectangle 1 (top): 3 m × 3 m = 9 m²
- Rectangle 2 (bottom): 2 m × 2 m = 4 m²
Total Area = 9 + 4 = 13 m²
Room B:
Let me trace around the outside to find the perimeter:
- Top edge: 2 m
- Right side: 4 m
- Bottom right: 3 m (going left)
- Bottom left vertical: 3 m (going down)
- Bottom left horizontal: 3 m (going left)
- Left side: 3 m (going up)
Perimeter = 2 + 4 + 3 + 3 + 3 + 3 = 18 m
For the area, I'll split it into two rectangles:
- Rectangle 1 (right): 2 m × 4 m = 8 m²
- Rectangle 2 (left): 3 m × 3 m = 9 m²
Total Area = 8 + 9 = 17 m²
Let me double-check my calculations:
Room A perimeter: 3 + 5 + 2 + 2 + 2 + 3 = 17 m ✓
Room A area: (3×3) + (2×2) = 9 + 4 = 13 m² ✓
Room B perimeter: 2 + 4 + 3 + 3 + 3 + 3 = 18 m ✓
Room B area: (2×4) + (3×3) = 8 + 9 = 17 m² ✓
Final Answer:
Room A: Perimeter = 17 m, Area = 13 m²
Room B: Perimeter = 18 m, Area = 17 m²
Room B has both the longest perimeter (18 m) and the largest area (17 m²).
Parent Tip: Review the logic above to help your child master the concept of area and perimeter of compound shapes worksheet.
