请解答这道题目---**Extraction Content:** **(2024秋·延庆区期末)** **Question Stem:** 在研究平行四边形面积时，我们经常用到割补法。割补法在我国古代数学著作中就有体现，三国时期魏国数学家刘徽称之为“以盈补虚”，以多余补不足，即“出入相补”。把一个面积是12cm²的直角三角形割补成一个长方形，这个长方形的长是4cm，原来三角形的高是 \_ 6 \_ cm。 **Mathematical Formulas/Equations:** Area of triangle = 12 cm² Area of rectangle = Area of triangle = 12 cm² Length of rectangle = 4 cm Area of rectangle = Length × Width 12 cm² = 4 cm × Width Width = 3 cm If the rectangle is formed by cutting the triangle parallel to its base and rearranging, the length of the rectangle is the base of the triangle and the width of the rectangle is half the height of the triangle. Let base of triangle = b, height of triangle = h. Area of triangle = (1/2) × b × h = 12 If Length of rectangle = b = 4 cm, then Width of rectangle = h/2. Area of rectangle = b × (h/2) = 4 × (h/2) = 2h. Since Area of rectangle = Area of triangle, 2h = 12. h = 6 cm. If the rectangle is formed by cutting the triangle along its height and rearranging, the length of the rectangle could be the height of the triangle and the width could be half the base. If Length of rectangle = h = 4 cm, then Width of rectangle = b/2. Area of rectangle = h × (b/2) = 4 × (b/2) = 2b. Since Area of rectangle = Area of triangle, 2b = 12. b = 6 cm. In this case, the height is 4 cm and the base is 6 cm. Area = (1/2) * 6 * 4 = 12 cm². This is also possible. However, the diagram usually illustrates the cut parallel to the base. Also, the provided answer "6 cm" aligns with the first scenario where the length of the rectangle is the base of the triangle. The question asks for the height of the original triangle. Based on the likely interpretation facilitated by the diagram and the provided value, the height is 6 cm. **Options:** No multiple-choice options (A, B, C, D) are present. The question has a blank space filled with "6 cm". **Other Relevant Text:** "(2024秋·延庆区期末)" indicates the source/exam information. Description of "割补法" (cut and paste method) and its origin and meaning ("以盈补虚", "出入相补"). Units: cm, cm². **Chart/Diagram Description:** * **Type:** Geometric illustration of a transformation process. * **Main Elements:** * A right-angled triangle is shown on the left. * A horizontal line segment cuts the triangle, dividing it into an upper triangular part and a lower trapezoidal part. The cut appears to be made approximately halfway up the height of the triangle, parallel to the base. * A curved arrow indicates a rotation of the upper triangular part in a clockwise direction. * The right side of the diagram shows a rectangle. * The rectangle is formed by the lower trapezoidal part of the original triangle and the rotated upper triangular part. The shaded area within the rectangle represents the rotated triangular piece, fitting into the space next to the trapezoidal piece to form a complete rectangle. * The diagram visually demonstrates how a triangle's area relates to a rectangle's area through cutting and rearrangement. The transformation shown specifically suggests that the base of the original triangle becomes the length of the resulting rectangle, and half the height of the original triangle becomes the width (or height) of the resulting rectangle.