Answer
(a) $\frac{P_{EGIK}}{P_{ABCD}} = \frac{\sqrt{5}}{3}$
(b) $\frac{A_{EGIK}}{A_{ABCD}} = \frac{5}{9}$
Work Step by Step
(a) Let each side of the square $ABCD$ be 3 units.
We can find the length of each side of the square $EGIK$:
$L = \sqrt{(1)^2+(2)^2}$
$L = \sqrt{1+4}$
$L = \sqrt{5}$
We can find the ratio:
$\frac{P_{EGIK}}{P_{ABCD}} = \frac{4\times \sqrt{5}}{4\times 3} = \frac{\sqrt{5}}{3}$
(b) We can find the ratio:
$\frac{A_{EGIK}}{A_{ABCD}} = \frac{(\sqrt{5})^2}{(3)^2} = \frac{5}{9}$
