1. **Problem Statement:** A circular clock has radius $r=20$ cm. A chord forms an equilateral triangle with two radii. We need to find the percentage area of the smaller segment created by this chord relative to the total circle area. 2. **Given:** - Radius $r=20$ cm - Triangle formed is equilateral, so each angle at center is $60^\circ$ - $\pi=3.14$, $\sqrt{3}=1.732$ 3. **Calculate total area of the circle:** $$\text{Area}_{circle} = \pi r^2 = 3.14 \times 20^2 = 3.14 \times 400 = 1256 \text{ cm}^2$$ 4. **Calculate area of the equilateral triangle formed by two radii and the chord:** - Side length of triangle = radius = 20 cm - Area of equilateral triangle formula: $$\text{Area}_{triangle} = \frac{\sqrt{3}}{4} s^2 = \frac{1.732}{4} \times 20^2 = 0.433 \times 400 = 173.2 \text{ cm}^2$$ 5. **Calculate area of the sector formed by the $60^\circ$ angle:** - Sector area formula: $$\text{Area}_{sector} = \frac{\theta}{360} \times \pi r^2 = \frac{60}{360} \times 1256 = \frac{1}{6} \times 1256 = 209.33 \text{ cm}^2$$ 6. **Calculate area of the smaller segment:** - Segment area = Sector area - Triangle area $$\text{Area}_{segment} = 209.33 - 173.2 = 36.13 \text{ cm}^2$$ 7. **Calculate percentage of the smaller segment area relative to the total circle area:** $$\text{Percentage} = \frac{36.13}{1256} \times 100 = 2.88\%$$ **Final answer:** The smaller painted segment represents approximately **2.88%** of the clock's total area.