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
5 identical rectangular tiles make a big rectangle, as shown:
1 lying down in the top row and 4 standing up in the bottom row, with no gaps.
The big rectangle has a perimeter of 54 cm.
What is the area of the big rectangle, in cm²?
Show the hints (2)
💡Hint 1: The top and bottom rows are the same length. How do a tile's length and width compare?
💡Hint 2: Call a tile's length 4 parts and its width 1. How many parts is the big rectangle's perimeter?
Worked solution
Have a go first, then read the solution step by step.
1.Both rows are the same length: 1 tile length = 4 tile widths, so length : width = 4 : 1.
2.Call the length 4 parts and the width 1. The big rectangle is 1 × 4 = 4 parts long and 4 + 1 = 5 parts wide.
3.The big rectangle's perimeter is (4 + 5) × 2 = 18 parts, so one part = 54 ÷ 18 = 3 cm.
4.The big rectangle is 12 cm by 15 cm: area 12 × 15 = 180 cm².
⚠️Common mistake: sharing out the perimeter or area before finding how the tile's length and width compare. The two rows being equal fixes that ratio.
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