Question

Determine:

a) a área da região hachurada II.
b) a área da região hachurada III

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo-a-passo:

$\sf A = \left(\dfrac{a}{2}\right)^2 \div 2$

$\sf A =\dfrac{a^2}{4} \div 2$

$\boxed{\boxed{\sf A = \dfrac{a^2}{8}\:u.a^2}} \leftarrow \textsf{REGIAO I}$

$\sf A = \dfrac{\pi \left(\dfrac{a}{2}\right)^2}{4} - \dfrac{a^2}{8}$

$\sf A = \dfrac{\pi \left(\dfrac{a^2}{4}\right)}{4} - \dfrac{a^2}{8}$

$\sf A = \dfrac{\pi a^2}{16} - \dfrac{a^2}{8}$

$\boxed{\boxed{\sf A = \dfrac{\pi a^2 - 2a^2}{16}\:u.a^2}} \leftarrow \textsf{REGIAO II}$

$\sf A = \left[\left(\dfrac{a\sqrt{2}}{2}\right)^2 - \dfrac{\pi a^2 - 2a^2}{4}}} - \pi \left(\dfrac{a\sqrt{2} - a}{2}\right)^2}\right] \div 4$

$\sf A = \left[\dfrac{2a^2}{4} - \dfrac{\pi a^2 - 2a^2}{4} - \dfrac{3\pi a^2 - 2\pi a^2\sqrt{2} }{4}\right] \div 4$

$\sf A = \left[\dfrac{2a^2 - \pi a^2 + 2a^2 - 3\pi a^2 + 2\pi a^2\sqrt{2} }{4} \right] \div 4$

$\sf A = \left[\dfrac{4a^2 - 4\pi a^2 + 2\pi a^2\sqrt{2} }{4} \right] \div 4$

$\sf A = \left[\dfrac{4a^2 - 4\pi a^2 + 2\pi a^2\sqrt{2} }{16} \right]$

$\boxed{\boxed{\sf A = \dfrac{2a^2 - 2\pi a^2 + \pi a^2\sqrt{2} }{8}\:u.a^2}} \leftarrow \textsf{REGIAO III}$