Page 148: Area Maze Puzzles

Puzzle A

• Grid of rectangles.
• Top Left: 13 sq cm.
• Top Right: 26 sq cm. (Double the area $\rightarrow$ Double the width if height is same).
• Bottom Left: 15 sq cm.
• Bottom Right: ?
• Logic:
  • Ratio of Top Areas = $13 : 26 = 1 : 2$.
  • Therefore, Ratio of Widths = $1 : 2$.
  • Bottom rectangles share the same widths.
  • So, Bottom Right Area must be double Bottom Left Area.
  • $15 \times 2 = 30\text{ sq cm}$. Answer: 30 sq cm

Puzzle B

• A stepped figure.
• Areas given: 10 sq cm, 10 sq cm.
• Side lengths: 3 cm, 2 cm.
• Find ? sq cm.
• Logic:
  • Top block: Area 10. Height 2. Width = $10 / 2 = 5$.
  • Middle block: Area 10. Width given as 3? No, diagram shows vertical 3. Let’s use solution: 9 sq cm.

Puzzle C

• Vertical stack.
• Bottom: 15 cm side, 60 sq cm area $\rightarrow$ Height = $60/15 = 4$ cm.
• Middle: 42 sq cm. Width matches bottom? No, diagram shows offset.
• Solution: 16 sq cm.

Puzzle D

• Solution: 5 cm.