Question

calcule a área da região sombreada

Answer 1

Resposta:

Explicação passo-a-passo:

Neste exercício devemos calcular a área maior e subtrair as áreas menores, desta forma teremos encontrado a área sombreada.

a)

$A_{Sombreada}=A_{C}-(A_{cm1}+A_{Cm2})\\A_{Sombreada}=\pi.r^2-(\pi.r^2+\pi.r^2)\\A_{Sombreada}=\pi.12^2-(\pi.6^2+\pi.6^2)\\A_{Sombreada}=144.\pi-(36.\pi+36.\pi)\\A_{Sombreada}=144.\pi-72.\pi\\\boxed{A_{Sombreada}=72.\pi\ u.a}$

b)

$r=\dfrac{D_C}{2}\\\\r=\dfrac{(16+16+6+6)}{2}\\r=\dfrac{44}{2}\\\\\boxed{r=22\ u.m.}$

$A_{Sombreada}=A_{C}-(A_{cm1}+A_{Cm2})\\A_{Sombreada}=\pi.r^2-(\pi.r^2+\pi.r^2)\\A_{Sombreada}=\pi.22^2-(\pi.16^2+\pi.6^2)\\A_{Sombreada}=484.\pi-(256.\pi+36.\pi)\\A_{Sombreada}=484.\pi-292.\pi\\\boxed{A_{Sombreada}=192.\pi\ u.a.}$

c)

$A_{Sombreada}=A_{Ret\^angulo}-A_{Trap\'ezio}\\\\A_{Sombreada}=b.h-\dfrac{(B+b).h}{2}\\\\A_{Sombreada}=12.6-\dfrac{(10+8).2}{2}\\\\A_{Sombreada}=72-\dfrac{(18).2}{2}\\A_{Sombreada}=72-18\\\boxed{A_{Sombreada}=54\ u.a.}$