An easy question on perimeter and area for P4–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
4 identical square cards, each with sides of 2 cm, are stuck together edge to edge to make the shape shown.
What is the perimeter of the shape, in cm?
Show the hints (2)
💡Hint 1: Where two cards touch, is that edge still on the shape's perimeter?
💡Hint 2: Walk round the outside of the shape and count the card edges you pass.
Worked solution
Have a go first, then read the solution step by step.
1.Walk round the outside of the shape. First count the edges across (orange): there are 4.
2.Then the upright edges (blue): there are 6.
3.That's 4 + 6 = 10 edges round the outside, each 2 cm, so the perimeter = 2 × 10 = 20 cm.
⚠️Common mistake: adding all 4 cards' perimeters, 8 × 4 = 32 cm. The 3 places where cards touch (green) are inside the shape, not on its perimeter.
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