GS. $1 A B C D$ is a parallelogram and $E$ is the midpoint of $C D$. If the ratio of the area of the triangle $A D E$ to the area of the parallelogram $A B C D$ is $1: a$, find $a$.

GS. $2 A B C D$ is a parallelogram and $E$ is the midpoint of $C D$. $A E$ and $B D$ meet at $M$. If $D M: M B=1: k$, find $k$.

GS. 3 If the square root of 5 is approximately 2.236 , the square root of 80 with the same precision is $d$. Find $d$.

GS. 4 A square is changed into a rectangle by increasing its length by $20 \%$ and decreasing its width by $20 \%$. If the ratio of the area of the rectangle to the area of the square is $1: r$, find $r$.
$$
\begin{array}{l}
1: a=1: 4 \\
a=4
\end{array}
$$

It is easy to show that $\triangle A B M \sim \triangle E D M$ (equiangular)
$$
\begin{array}{l}
D M: M B=D E: A B=1: 2 \\
k=2 \\
\sqrt{80}=\sqrt{16 \times 5}=4 \sqrt{5}=4 \times 2.236=8.944
\end{array}
$$

Let the side of the square be $x$
Ratio of areas $=1.2 x \cdot 0.8 x: x^{2}$
$$
\begin{aligned}
\quad=0.96: 1=1: \frac{25}{24} \\
r=\frac{25}{24}
\end{aligned}
$$