#### Answer

(a) $P = 4 \sqrt{5}$
(b) $P = 6\sqrt{2}$

#### Work Step by Step

(a) We can find the length of each side of the quadrilateral $EGIK$:
$L = \sqrt{(1)^2+(2)^2}$
$L = \sqrt{1+4}$
$L = \sqrt{5}$
We can find the perimeter:
$P = 4L = 4 \sqrt{5}$
(b) We can find the length of the side $EH$ of the quadrilateral $EHIL$:
$L_1 = \sqrt{(2)^2+(2)^2}$
$L_1 = \sqrt{4+4}$
$L_1 = \sqrt{8}$
$L_1 = 2\sqrt{2}$
We can find the length of the side $HI$ of the quadrilateral $EHIL$:
$L_2 = \sqrt{(1)^2+(1)^2}$
$L_2 = \sqrt{1+1}$
$L_2 = \sqrt{2}$
We can find the perimeter:
$P = 2L_1+2L_2$
$P = (2\times 2\sqrt{2})+(2 \times \sqrt{2})$
$P = 6\sqrt{2}$