f a seven-sided polygon is divided into triangles, by drawing all diagonals from one vertex, how many triangles would be there?
Answers
Step-by-step explanation:
in the case of a regular polygons , the formula for the number of a triangles in a polygon is:number of triangle= n -2(where n is the number of sides or vertices)
Why? the triangles are created by drawing the diagonals from one vertex to all the others. since there would be no diagonal draw back to itself, and the diagonals to each adjacent vertex would lie on top of the adjacent sides, the number of diagonals from a single vertex is 3 less than the number of sides, or n -3 . the the number of triangles is one more than that, so n-2.
this can be used as another way to calculate the sum of the interior angles of a polygon. the interior angles of a triangle always sum to 180° . the the number of triangles is n-2 (above).
therefore the interior angles of a polygon must be the sum of all the triangles, interior angles,or 180(n-2).
in the case of irregular polygon.
for convex, irregular polygons, dividing it into triangles can help if you trying to find its area . for example, in the figure of right polygon, it may be possible to find the area area of each triangle and then sum them......