There is a hexagon ABCDEF as shown in a figure below.
How many ways of method of the division which divides this hexagon into three parts by two diagonal lines is there in all?
How many ways of method of the division which divides this hexagon into three parts by two diagonal lines is there in all?
Answer
21 ways
Solution
There are two cases to divide a hexagon into three parts by two diagonal lines as follows.
① Draw two diagonal lines from the one vertex
② Draw two diagonal lines not crossing from different vertex
① Three diagonal lines can be drawn from one vertex.
The number of ways of drawing two diagonal lines from one vertex turns into the number of ways of choosing two lines among three lines.
It is 3 × 2 / (2 × 1) = 3 ways.
Since there are six vertex,there are 3 x 6 = 18 ways in all.
21 ways
Solution
There are two cases to divide a hexagon into three parts by two diagonal lines as follows.
① Draw two diagonal lines from the one vertex
② Draw two diagonal lines not crossing from different vertex
① Three diagonal lines can be drawn from one vertex.
The number of ways of drawing two diagonal lines from one vertex turns into the number of ways of choosing two lines among three lines.
It is 3 × 2 / (2 × 1) = 3 ways.
Since there are six vertex,there are 3 x 6 = 18 ways in all.
② There is three groups of the diagonal lines of AC and FD, AE and BD, BF and CE.
The sum total above is 18 + 3 = 21 ways.
