The height of a regular prism is 12 cm. The side of its base is 6 cm. Calculate the perimeter of the prism section

The height of a regular prism is 12 cm. The side of its base is 6 cm. Calculate the perimeter of the prism section by a plane containing a straight line and the middle of an edge.

1. From the section of the plane it follows that:
D1F = DF, C1E = EC.
2. FE II CD;
FE = CD = 12 cm;
3. Consider triangle AFD.
AD = 12 cm;
FD = 5 cm;
angle FDA = 90 °;
Find AF:
AF = √12 ^ 2 + 5 ^ 2;
AF = √169;
AF = 13 cm;
4. Find the perimeter of the prism section:
P = AB + BE + EF + AF;
P = 2 * AB + 2 * AF;
P = 2 * 12 + 2 * 13;
P = 50 cm;
Answer: P = 50 cm;