The image you've uploaded contains several mathematical tasks related to pyramids. Let's break them down and analyze them step by step.

1. Task 1: The sides of the base of a regular hexagonal pyramid are given as 10, and the slant height (lateral edge) is 13. The goal is to find the surface area of the pyramid.

2. Task 2: You need to find the surface area of a regular square pyramid with base side length 20 and height 24.

3. Task 3: In a triangular pyramid ABCP, the point P is the apex, M is the midpoint of the edge BC, AB = 6, and the lateral surface area is 126. The objective is to find the length of the segment PM.

4. Task 4: In a pyramid ABCP, the lateral edges PA and AC are perpendicular to the base ABC, and the angle between the edges PA and the base plane is 60°. The goal is to calculate the surface area of the lateral faces of the pyramid.

5. Task 5: The base of the pyramid is a right-angled triangle ABC, with right angle at C. The base sides BC = 5, and the angle at A is 30°. The lateral edge is inclined at 60° to the base. The goal is to find the height of the pyramid.

I can provide solutions for each of these problems. Which one would you like to start with? Feel free to let me know if you'd like a detailed explanation of any part of the problems!