求解---**Extraction Content:** **Question:** 6. 【面积与旋转】 如图所示, 直角三角形 ABC 的斜边 AB 长为 10 厘米, ∠ABC=60°, 此时 BC 长 5 厘米. 以点 B 为中心, 将 △ABC 顺时针旋转 120°, 点 A、C 分别到达点 E、D 的位置. 求 AC 边扫过的图形即图中阴影部分的面积. (π取 3) **Textual Information:** * Question Number: 6. * Topic/Category: 面积与旋转 (Area and Rotation). * Problem Description: As shown in the figure, in right-angled triangle ABC, the hypotenuse AB has a length of 10 cm, ∠ABC = 60°, and at this time BC has a length of 5 cm. With point B as the center, rotate △ABC clockwise by 120°, points A and C respectively reach the positions of points E and D. Find the area of the figure swept by side AC, which is the shaded part in the figure. (Take π as 3) **Chart/Diagram Description:** * Type: Geometric figure (Not provided in the image, but referenced in the text "如图所示" - As shown in the figure). * Main Elements (Based on text description, the figure likely contains): * Triangle ABC: Right-angled triangle. * Point B: Rotation center. * Point A, C: Vertices of the triangle. * Line segment AB: Hypotenuse, length 10 cm. * Line segment BC: Length 5 cm. * Angle ABC: 60 degrees. * Rotated Triangle BED: Result of rotating triangle ABC about B. * Point E: Rotated position of A. * Point D: Rotated position of C. * Rotation: Clockwise rotation around B by 120 degrees. * Shaded region: The area swept by the line segment AC during the rotation. This area is likely bounded by arcs AE, CD and segments AC, ED. **Other Relevant Text:** * Instruction for pi: (π取 3) - Take π as 3.