SOLUTION: Please help me with this. "Suppose you know the number of sides in a regular polygon, the lenght of each side, and the distance from each side to the centre. How can you determi

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You can always make a bunch of little triangles and then find the area of each one Area = base*height/2. Then add the results.
Since your polygon is regular, each triangle will have the same area - so the answer is even easier. Just find the area of one triangle and then multiply by the number of sides in the polygon (which is the same as the number of little triangles)

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If you take one side of a regular polygon and the two segments that connect the endpoints of the side to the center, you will have formed a triangle. The length of the side of the polygon is the base of the triangle and the distance from the side to the center is the altitude or height of the triangle. Since there is one of these triangles for every side of the polygon, the total area of the polygon is the number of sides times the area of the triangle. The area of one triangle is where b is the length of the base and h is the height. The area of the entire polygon is then where n is the number of sides.