Question

Сколько всего диагоналей можно провести в пятиугольнике, в девятиугольнике, в п-угольнике, где п -3?

Answer 1

Формула  диагоналей многоугольника:

d = (n(n-3))/2

где d - число диагоналей, n - число сторон многоугольника

в пятиугольнике,

d = (5(5-3))/2=(5*2)/2=5

в девятиугольнике,

d = (9(9-3))/2=(9*6)/2=27

в п-угольнике, где п -3

у треугольника нет диагоналей, формула не применима ,но если требуется подставить то будет 0

d = (0(0-3))/2=(0*-3)/2=0

Answer 2

Diagonals in a Pentagon (5-sided polygon)

To determine the number of diagonals that can be drawn in a pentagon, we can use the formula:

Number of diagonals in an n-sided polygon = n(n-3)/2.

For a pentagon (5-sided polygon), the formula becomes:

Number of diagonals in a pentagon = 5(5-3)/2 = 5(2)/2 = 5.

Therefore, there are 5 diagonals that can be drawn in a pentagon.

Diagonals in a Nonagon (9-sided polygon)

Using the same formula, we can calculate the number of diagonals in a nonagon (9-sided polygon):

Number of diagonals in a nonagon = 9(9-3)/2 = 9(6)/2 = 27.

Therefore, there are 27 diagonals that can be drawn in a nonagon.

Diagonals in a p-gon (p = 3)

Now, let's consider a p-gon where p = 3. Using the formula mentioned earlier, we can calculate the number of diagonals in a triangle:

Number of diagonals in a triangle = 3(3-3)/2 = 3(0)/2 = 0.

Therefore, there are no diagonals that can be drawn in a triangle.

In summary: - A pentagon has 5 diagonals. - A nonagon has 27 diagonals. - A triangle has no diagonals.

I hope this answers your question! Let me know if you need further clarification.