A medium question on perimeter and area for P5, with a step-by-step solution, diagrams and the answer. Common in the Hua Xia Cup's P4 to P6 papers; harder ones work out areas from the ratios between triangles' areas.
The question
2 identical square sheets of paper have sides of 8 cm.
They are pinned to a noticeboard in a slanting line from top left to bottom right, each partly covering the one before, and each pair of neighbours overlaps in a square of the same size, as shown.
The perimeter of the whole shape is 56 cm.
What is the area of each overlap, in cm²?
Show the hints (2)
💡Hint 1: Slide the stepped edges: the whole outline has a big square's perimeter. What is that square's side?
💡Hint 2: The big square's side = 8 cm + (2 − 1) × how far each extra sheet reaches out.
Worked solution
Have a go first, then read the solution step by step.
1.Slide the stepped edges across up and down and the upright ones left and right: they make a big square, with the same perimeter. Its side is 56 ÷ 4 = 14 cm.
2.The big square's side = one sheet's side + 1 × how far each extra sheet reaches out, so each reaches 14 − 8 = 6 cm.
3.The overlap square's side = 8 − 6 = 2 cm, so its area is 2 × 2 = 4 cm².
⚠️Common mistake: taking the 6 cm each sheet reaches out as the overlap's side. The overlap's side is 8 minus that.
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