Equal division refers to the symmetrical and equivalent division of geometric figures, in which there are both lines and faces. In order to realize bisection, the region is divided into many corresponding graphics, mainly axisymmetric graphics.
Bisector: Two rays emanating from the vertex of an angle. If an angle is divided into three equal angles, these two rays are called the bisector of the angle.
If it is the bisector of an angle: divide an angle into three parts with two lines, then those two lines are bisectors.
If it is the bisector of side length: divide an edge into three equal points and the connecting line corresponding to the vertex of this edge.
Application definition
Find the area of the regular hexagon of the figure 1 in the atlas 1. (unit: cm) Analysis and solution Divide a regular hexagon into three parallelograms as shown in Figure 2: Atlas 1. Therefore, the area of a regular hexagon is: 37.5×(65÷2)×3=3656.25 (square centimeter). Example 2 is shown in Figure 3, Atlas 1, and two equilateral identical quadrangles partially overlap at the midpoint of both sides. It is known that the area of the overlapping part is 8 square centimeters. Find the area of the shaded part.