Frequency polygon is a closed figure got by joining the Middle points of the top of rectangles of histograms. The extremes are joined with X-axis at a distance of half the length of class-interval from the extremes of the variable of the class-interval.
Image Source: palomar.edu/users/rmorrissette/Lectures/Stats/Graphing/FreqPolygon2.jpg
It can be constructed by taking middle points of class intervals on X-axis and the frequency on Y-axis. These points are joined. Two extremes are joined with base in such a way that they touch the X-axis at half the distance of class interval outside the extreme points.
If we have to construct histogram and frequency polygon both, then we have to join the mid points of the tops of all the rectangles and finally two extreme points with the points outside the extreme rectangles.