Discussion
A man walks entirely around his semi-circular garden. What is the area of his garden, if he walks 324m?
Answer: B
Walking entirely around a semicircular garden means covering the curved arc and the straight diameter.
\[ \text{perimeter} = \pi r + 2r = r(\pi + 2) \]
With \( \pi = \tfrac{22}{7} \), so \( \pi + 2 = \tfrac{36}{7} \):
\[ r \times \frac{36}{7} = 324 \quad\Longrightarrow\quad r = \frac{324 \times 7}{36} = 63 \text{ m} \]
\[ A = \frac{1}{2}\pi r^{2} = \frac{1}{2} \times \frac{22}{7} \times 3969 = 6237 \text{ m}^{2} \]
Omitting the straight edge would make the perimeter \( \pi r \) alone and give a radius of 103 m - the diameter is a real part of the boundary he walks.
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