Subjects geometry

Luas Tembereng 0A9Fdb

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1. **Stating the problem:** We are asked to find the area of the shaded segment (tembereng) of a circle with radius $r = 10$ cm and $\pi = 3.14$. 2. **Formula and explanation:** The area of a segment (tembereng) of a circle is given by: $$\text{Area segment} = \text{Area sector} - \text{Area triangle}$$ Where: - Area sector = $\frac{\theta}{360} \times \pi r^2$ - Area triangle depends on the chord and radius, but if the central angle $\theta$ is known, the triangle area can be calculated using: $$\text{Area triangle} = \frac{1}{2} r^2 \sin(\theta)$$ 3. **Important rules:** - $\theta$ is the central angle in degrees. - $r$ is the radius of the circle. 4. **Intermediate work:** The problem does not explicitly give the central angle $\theta$, but since the options are given, we assume the shaded area corresponds to a known segment. Let's check if the shaded area corresponds to half the circle minus a triangle or a known fraction. Since the radius $r=10$ cm, the full circle area is: $$\pi r^2 = 3.14 \times 10^2 = 314 \text{ cm}^2$$ The options are much smaller, so likely the segment corresponds to a smaller angle. Let's try to find the angle $\theta$ that matches the given options. For example, option B is 78.5 cm². Let's check if this corresponds to a quarter circle segment: Area sector for $\theta=90^\circ$: $$\frac{90}{360} \times 314 = \frac{1}{4} \times 314 = 78.5 \text{ cm}^2$$ If the triangle area is zero (like a quarter circle sector), the segment area equals sector area. So, the shaded area is likely a quarter circle segment. 5. **Final answer:** The area of the shaded segment (tembereng) is: $$\boxed{78.5 \text{ cm}^2}$$ Corresponding to option B.