The area of any polygon is the sum of the areas of the triangles it can be divided into. The calculation is easier in a regular polygon as it can be divided into identical triangles. One of the points (vertices) of the triangle is the centre of the polygon and the other two are two consecutive vertices of the polygon. The height of each of these triangles (apothem) is the perpendicular line from the centre of the polygon to one of its sides. Therefore, we can work out the area of each triangle by multiplying the length of the side by half of the apothem. If we multiple this result by the numbers of sides we can work out the area of a regular polygon: the perimeter multiplied by half the apothem.

2.- Repeat the exercise for a 15-sided polygon whose sides are 2 units long and a 25-sided polygon whose sides are 1.5 units long. Use the length of the apothem, which is given in each case, to help you and check your results with the values of the areas given in the window. 

3.- Try and work out the length of the apothem yourself for a square and hexagon whose sides are 5 units long and check your answers in the window.