Subjects geometry

Heart Area 70282B

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1. **State the problem:** Find the area of the colored part of the figure in problem 3, which is a heart shape with a dimension labeled 5 cm. 2. **Understand the figure and given data:** The heart shape is symmetric and the given dimension is 5 cm, which we interpret as a key length (likely width or radius of arcs forming the heart). 3. **Formula and approach:** The heart shape can be approximated by combining geometric shapes such as circles and triangles or by using known formulas for heart shapes. Since no explicit formula is given, we assume the heart is formed by two semicircles of radius 2.5 cm (half of 5 cm) and a triangle below. 4. **Calculate the area of the two semicircles (which form a full circle):** $$\text{Radius} = \frac{5}{2} = 2.5\text{ cm}$$ $$\text{Area of full circle} = \pi r^2 = \pi \times (2.5)^2 = 6.25\pi\text{ cm}^2$$ 5. **Calculate the area of the triangle below the semicircles:** Assuming the triangle is equilateral or isosceles with base 5 cm and height 5 cm (approximation for heart shape), $$\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 5 = 12.5\text{ cm}^2$$ 6. **Calculate total area of the heart shape:** $$\text{Total area} = 6.25\pi + 12.5 \approx 6.25 \times 3.1416 + 12.5 = 19.635 + 12.5 = 32.135\text{ cm}^2$$ 7. **Final answer:** The area of the colored heart shape is approximately $$\boxed{32.14\text{ cm}^2}$$