Question

calcula el área de la región sombreada mostrada​

Answer 1

Hola (｡•̀ᴗ-)✧

Respuesta:

A = (18√2 - 9)π

Explicación paso a paso:

radio del cuadrante:

$R \: = \: 6+6\sqrt{2} \: =\: 6(1+\sqrt{2})$

A.sombreada = A.cuadrante - A.circulo

${A = \frac{\bigl ( 6 (1+\sqrt{2} ) \bigr ) ^2 }{4} \pi - 6^2 \pi }$

${A = \frac{ 6^2 (1+\sqrt{2} )^2 }{4} \pi - 36\pi }$

${A = \frac{ 36 (1+2\sqrt{2} +2) }{4} \pi - 36\pi }$

${A = \frac{ 36 (3+2\sqrt{2}) }{4} \pi - 36\pi }$

${A = 9(3+2\sqrt{2}) \pi - 36\pi }$

${A = (27+18\sqrt{2}) \pi - 36\pi }$

${A = (18\sqrt{2}+27-36) \pi }$

${A = (18\sqrt{2}-9) \pi }$