Geometry and TrigonometryMediumArea of a border around a rectangle
Geometry and Trigonometry practice question
A rectangular garden measures 10 metres by 6 metres. A path of uniform width 1 metre runs around the outside of the garden. What is the area, in square metres, of the path?
Answer: 36
The path adds 1 metre on every side, so the outer rectangle is 12 metres by 8 metres. Path area = outer area − garden area = 12 × 8 − 10 × 6 = 96 − 60 = 36.
Common wrong answers
- If you answered 17
- 17 comes from an 11 × 7 outer rectangle — adding 1 metre to each dimension only once. The path is on BOTH sides, so each dimension grows by 2.
- If you answered 60
- 60 is the garden itself, not the path.
- If you answered 96
- 96 is the area of the outer rectangle, garden included. Subtract the garden's 60.
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