Question

determine a medida da área de cada uma destas figuras.

me ajudem por favorr

Answer 1

a)

$Area~=~(3\sqrt{8}+1)~.~(\sqrt{2}+3)\\\\\\Area~=~(3\sqrt{2~.~2^2}+1)~.~(\sqrt{2}+3)\\\\\\Area~=~(3~.~2\sqrt{2}+1)~.~(\sqrt{2}+3)\\\\\\Area~=~(6\sqrt{2}+1)~.~(\sqrt{2}+3)\\\\\\Area~=~6\sqrt{2}~.~\sqrt{2}~+~6\sqrt{2}~.~3~+~1~.~\sqrt{2}~+~1~.~3\\\\\\Area~=~6\sqrt{2}^2~+~18\sqrt{2}~+~\sqrt{2}~+~3\\\\\\Area~=~6~.~2~+~19\sqrt{2}~+~3\\\\\\\boxed{Area~=~(19\sqrt{2}~+~15)\,cm^2}$

b)

$Area~=~(\sqrt{20}+2)~.~(2\sqrt{5}-1)\\\\\\Area~=~(\sqrt{2~.~2~.~5}+2)~.~(2\sqrt{5}-1)\\\\\\Area~=~(\sqrt{2^2~.~5}+2)~.~(2\sqrt{5}-1)\\\\\\Area~=~(2\sqrt{5}+2)~.~(2\sqrt{5}-1)\\\\\\Area~=~2^2\sqrt{5}^2~+~2\sqrt{5}~.~(-1)~+~2~.~2\sqrt{5}~+ 2~.~(-1)\\\\\\Area~=~4~.~5~-~2\sqrt{5}~+~4\sqrt{5}~-~2\\\\\\Area~=~20~+~2\sqrt{5}~-~2\\\\\\\boxed{Area~=~(2\sqrt{5}~+~18)\,cm^2}$