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
Siu Yan builds a model winners' podium from three rectangular blocks side by side; its front is shown.
The bottom edge of the front is 13 cm long, the tallest block, in the middle, is 11 cm high, and every corner is a right angle.
What is the perimeter of the whole front of the podium, in cm?
Show the hints (2)
💡Hint 1: The story doesn't say how tall the two side blocks are. Do you really need to know?
💡Hint 2: Slide the three top edges up. How tall are the two upright pieces on the left together? And on the right?
Worked solution
Have a go first, then read the solution step by step.
1.Sliding the three top edges up makes one edge 13 cm long.
2.The two upright pieces on the left (the left block's height, plus the part of the middle block above it) slide left and add up to exactly 11 cm; the two on the right slide right and make 11 cm too.
3.So the perimeter is that of a 13 cm by 11 cm rectangle: (13 + 11) × 2 = 48 cm.
⚠️Common mistake: adding up the three blocks' perimeters. The edges where blocks touch are inside the shape, not on its perimeter.
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