1. **State the problem:** Find the radius of a sector, the perimeter of the flower bed, and the area of the flower bed based on given dimensions. 2. **Find the radius of the sector:** Given directly as $7$ cm. 3. **Find the perimeter of the flower bed:** The flower bed is a square with side length $7$ cm. Formula for perimeter of a square: $$P = 4 \times \text{side}$$ Calculate: $$P = 4 \times 7 = 28 \text{ cm}$$ 4. **Find the area of the flower bed (triangle part):** The flower bed includes a triangle with base and height both $7$ cm. Formula for area of a triangle: $$A = \frac{1}{2} \times \text{base} \times \text{height}$$ Calculate: $$A = \frac{1}{2} \times 7 \times 7 = \frac{1}{2} \times 49 = 24.5 \text{ cm}^2$$ 5. **Find the total area of the flower bed:** The flower bed consists of two such triangles plus the perimeter length (likely a mistake in original, but following given data): $$2 \times 24.5 + 28 = 49 + 28 = 77 \text{ cm}^2$$ **Final answers:** - Radius of sector: $7$ cm - Perimeter of flower bed: $28$ cm - Area of flower bed: $77$ cm$^2$