Subjects geometry

Area Approximation 69F3D3

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1. **Stating the problem:** We are asked to find the approximate area of a shape drawn on a grid where each square measures 1 cm by 1 cm. 2. **Understanding the problem:** The shape is roughly elliptical and spans about 5 squares wide and 4 squares tall. 3. **Formula for area of an ellipse:** $$\text{Area} = \pi \times a \times b$$ where $a$ and $b$ are the semi-major and semi-minor axes respectively. 4. **Identify $a$ and $b$:** - The width is about 5 cm, so the semi-major axis $a = \frac{5}{2} = 2.5$ cm. - The height is about 4 cm, so the semi-minor axis $b = \frac{4}{2} = 2$ cm. 5. **Calculate the area:** $$\text{Area} = \pi \times 2.5 \times 2 = 5\pi$$ 6. **Approximate the value:** $$5\pi \approx 5 \times 3.14 = 15.7 \text{ cm}^2$$ 7. **Compare with given options:** The closest option to 15.7 cm² is not listed, but since the shape is approximate, the best choice among (A) 23 cm², (B) 27 cm², and (C) 30 cm² is (A) 23 cm² as it is the smallest and closest. **Final answer:** Approximately 23 cm² (Option A).