Question

COMO FAÇO O CALCULO?

DIAGONAIS
N=31 ???

SI=180(N-2)

AI=

(N-2) <<< ???
(N-3) ???
ME AJUDEEEEEEM?

Answer 1

Resolução da questão, veja:

$\mathsf{D = \dfrac{N~\cdot~(N-3)}{2}}~\to~\mathsf{N=31}}\\\\\\\\ \mathsf{D=\dfrac{31~\cdot~(31-3)}{2}}\\\\\\\\ \mathsf{D = \dfrac{31~\cdot~28}{2}}\\\\\\\\\ \mathsf{D= \dfrac{868}{2}}\\\\\\\\\ \large\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\mathsf{D = 434.}}}}}}}}}}}}}}}}}}}}}}}}$

Ou seja, esse polígono de 31 lados possui 434 Diagonais.

Espero que te ajude '-'