Question

Calcule o numeo de diagonais de um :
A) decógono
B) dodecàgono
C)eneagono
D) triângolo

Answer 1

a)

Um decágono possui 10 lados

$d_{n}=\dfrac{n(n-3)}{2}\\\\\\d_{10}=\dfrac{10(10-3)}{2}\\\\\\d_{10}=\dfrac{10\cdot7}{2}\\\\\\\boxed{\boxed{d_{10}=35}}$

b)

Um dodecágono possui 12 lados

$d_{n}=\dfrac{n(n-3)}{2}\\\\\\d_{12}=\dfrac{12(12-3)}{2}\\\\\\d_{12}=\dfrac{12\cdot9}{2}\\\\\\\boxed{\boxed{d_{12}=54}}$

c)

Um eneágono possui 9 lados

$d_{n}=\dfrac{n(n-3)}{2}\\\\\\d_{9}=\dfrac{9(9-3)}{2}\\\\\\d_{9}=\dfrac{9\cdot6}{2}\\\\\\\boxed{\boxed{d_{9}=27}}$

c)

Um triângulo possui 3 lados, e o triângulo não possui diagonais.

$d_{n}=\dfrac{n(n-3)}{2}\\\\\\d_{3}=\dfrac{3(3-3)}{2}\\\\\\d_{3}=\dfrac{3\cdot0}{2}\\\\\\\boxed{\boxed{d_{3}=0}}$