Triangles are three-sided polygons that come in three types based on their side lengths: equilateral triangles have all three sides the same length, isosceles triangles have two sides the same length, and scalene triangles have all three sides of different lengths. The area of any triangle can be calculated using Hero's Formula, which uses the triangle's side lengths and semi-perimeter. While Pascal's Triangle is named after Blaise Pascal, he did not invent the triangle - other mathematicians studied and used triangular patterns before him.