Question 815167
The interior angles of a polygon with N sides add up to
{{{(N-2)*180^o}}} .
In this case,
{{{(N-2)*180=1260}}} --> {{{N-2=1260/180}}} --> {{{N-2=7}}} --> {{{N=9}}} .
So we are dealing with a polygon with 9 sides.
One of the formulas to calculate the area of a polygon is
{{{Area = perimeter*apothem/2=N*side*apothem/2}}} ,
where apothem is the segment or the distance from  the center of the polygon to the center of one of its sides.
That "formula" comes from adding up the area of the N isosceles triangles formed by connecting the vertices to the center of the polygon.
The apothem (meaning the distance, the length of the apothem segment) can be calculated as
{{{(side/2)/tan(180^o/N)}}} .
In turn, the length of a side can be calculated from the perimeter and N as
{{{side=perimeter/N}}}
The whole calculation can be done step by step, or put together as one fancy formula.
{{{45/9=5}}} is the side (in cm)
{{{180/9=20}}}
{{{tan(20^o)=0.36397}}}
{{{5/2/0.36397=6.8687}}} is the apothem (in cm), and the area is
{{{45*6.8687/2=154.6}}} square centimeters.