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
A square photo sits in a square frame.
The wooden frame is 2 cm wide on every side, as shown.
The wood has an area of 120 cm².
What is the area of the photo, in cm²? (Not drawn to scale.)
Show the hints (2)
💡Hint 1: The wooden frame is an awkward shape. Could you cut it into 4 identical pieces?
💡Hint 2: Cut it pinwheel-wise into 4 identical rectangles, each 2 cm wide. How does their length compare with the side of the photo?
Worked solution
Have a go first, then read the solution step by step.
1.Cut the wood into 4 identical rectangles round the photo like a pinwheel (orange): each is 2 cm wide and as long as the photo's side + 2 cm.
2.Each rectangle's area = 120 ÷ 4 = 30 cm².
3.Each rectangle's length = area ÷ width = 30 ÷ 2 = 15 cm.
4.The rectangle's length includes a 2 cm corner, so the photo's side = 15 − 2 = 13 cm, and its area is 13 × 13 = 169 cm².
⚠️Common mistake: taking 30 ÷ 2 = 15 as the photo's side. Each rectangle also runs 2 cm on past it, round the corner; take that off.
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