Semicircular park — A railing of 288 m is used to fence a semicircular park (π = 22/7). Find the area of the park.

Introduction / Context:
The fence length around a semicircle equals the semicircle perimeter P = πr + 2r. From this we can find the radius r and then compute the area of the semicircle, A = (1/2) * π * r^2.

Given Data / Assumptions:

• Total railing (perimeter) P = 288 m
• π = 22/7
• Semicircle perimeter P = πr + 2r
• Semicircle area A = (1/2) * π * r^2

Concept / Approach:
Solve r from 288 = r(π + 2). Then compute A using the semicircle area formula with r obtained and π = 22/7.

Step-by-Step Solution:
π + 2 = 22/7 + 2 = 22/7 + 14/7 = 36/7r = 288 / (36/7) = 288 * 7 / 36 = 56 mA = (1/2) * π * r^2 = (1/2) * (22/7) * 56^2 = (11/7) * 3136 = 448 * 11 = 4928 m2

Verification / Alternative check:
Check perimeter with r = 56: P = (22/7)*56 + 112 = 176 + 112 = 288 m ✔

Why Other Options Are Wrong:
9865, 8956, and 9856 m2 are not consistent with r = 56; they reflect arithmetic slips; 4480 m2 forgets the exact factor (11/7) * r^2.

Common Pitfalls:
Using full-circle perimeter 2πr or omitting the diameter when computing a semicircle’s perimeter.

Final Answer:
4928 m2