(Originais Teachy 2023) - Question Hard of Mathematics

In an architecture project, an engineer needs to determine the amount of material needed to cover the facade of a building with a specific tile pattern. The tile design is a regular polygon that can be inscribed in a circle with a radius of 10 cm, and the tile shape is such that for each tile placed, there is an empty space of 5 cm between them. Knowing that the front view of the facade is a regular pentagon and that the distance from the top vertex to the center of the circle containing the tile is 15 cm, calculate: 1) The length of the side of the pentagon representing the front view of the facade. 2) The total area of the front view of the facade that will be covered by tiles. Consider that the regular pentagon is a right prism of infinite height and that the ground floor is a plan projection of the base of the prism.