1. **State the problem:** We need to find the area of the yellow shape formed by two intersecting circles where the angle between the two radii is 100° and the distance between the intersection points is 3.2 cm. 2. **Identify the shape:** The yellow shape is the lens-shaped intersection (also called a lune) of two circles with equal radii. The angle between the radii is given as $100^\circ$. 3. **Formula for the area of a circular segment:** The area of a segment of a circle with radius $r$ and central angle $\theta$ (in radians) is $$\text{Segment area} = \frac{r^2}{2}(\theta - \sin\theta)$$ 4. **Convert angle to radians:** $$\theta = 100^\circ = \frac{100 \pi}{180} = \frac{5\pi}{9}$$ 5. **Find the radius $r$:** The distance between the two intersection points is the chord length $c = 3.2$ cm. The chord length relates to radius and angle by $$c = 2r \sin\left(\frac{\theta}{2}\right)$$ So, $$r = \frac{c}{2 \sin(\theta/2)} = \frac{3.2}{2 \sin(50^\circ)}$$ Calculate $\sin(50^\circ) \approx 0.7660$, so $$r = \frac{3.2}{2 \times 0.7660} = \frac{3.2}{1.532} \approx 2.09 \text{ cm}$$ 6. **Calculate the area of one segment:** $$A_{segment} = \frac{r^2}{2}(\theta - \sin\theta) = \frac{(2.09)^2}{2} \left(\frac{5\pi}{9} - \sin\left(\frac{5\pi}{9}\right)\right)$$ Calculate $r^2 = 4.3681$, $\sin(100^\circ) = \sin(\frac{5\pi}{9}) \approx 0.9848$, so $$A_{segment} = \frac{4.3681}{2} (1.7453 - 0.9848) = 2.18405 \times 0.7605 = 1.660 \text{ cm}^2$$ 7. **Calculate the total lens area:** The lens is made of two such segments, so $$A_{lens} = 2 \times A_{segment} = 2 \times 1.660 = 3.32 \text{ cm}^2$$ **Final answer:** The area of the yellow shape is approximately **3.32 cm²**.