An oblong piece of ground measures 19m 2.5 dm by 12 m 5 dm. From center of…
2025
An oblong piece of ground measures 19m 2.5 dm by 12 m 5 dm. From center of each side of the ground, a path 2m wide goes across to the center of the opposite side. What is the area of the path?
- A.
59.5 m^2
- B.
54 m^2
- C.
34 m^2
- D.
78.54 m^2
Attempted by 4 students.
Show answer & explanation
Correct answer: A
Step 1: Convert dimensions to metres: 19 m 2.5 dm = 19 + 2.5×0.1 = 19.25 m; 12 m 5 dm = 12 + 5×0.1 = 12.5 m.
Step 2: Visualise the paths:
One path is a rectangle of length 19.25 m and width 2 m (area = 19.25×2).
The other path is a rectangle of length 12.5 m and width 2 m (area = 12.5×2).
They cross at the centre, overlapping in a 2 m × 2 m square (area = 4 m²) which would otherwise be counted twice.
Step 3: Compute areas and subtract overlap:
Area of first path = 19.25 × 2 = 38.5 m².
Area of second path = 12.5 × 2 = 25 m².
Overlap area = 2 × 2 = 4 m².
Total area of the path = 38.5 + 25 − 4 = 59.5 m².
Answer: 59.5 m²