A rectangular grassy plot is 112 m by 78 m. It has a gravel path 2.5 m m wide…
2024
A rectangular grassy plot is 112 m by 78 m. It has a gravel path 2.5 m m wide all around it on the inside. Find the area of the path?
- A.
952 m^2
- B.
912 m^2
- C.
925 m^2
- D.
950 m^2
Attempted by 10 students.
Show answer & explanation
Correct answer: C
Solution: Find the area of the gravel path by subtracting the inner grassy area from the total outer area.
Outer area = 112 × 78 = 8,736 m².
Each dimension of the inner grassy rectangle is reduced by 2 × 2.5 = 5 m, so inner dimensions = 107 m by 73 m.
Inner area = 107 × 73 = 7,811 m².
Area of the path = Outer area − Inner area = 8,736 − 7,811 = 925 m².
Alternative (shortcut) formula:
Area of path = 2w(L + B) − 4w² where w = path width, L and B are outer lengths.
Compute: 2·2.5·(112 + 78) − 4·(2.5)² = 950 − 25 = 925 m².
Therefore, the area of the gravel path is 925 m².