## Task 3 - 250623

Let $A B C D$ be a square with side length $14 \mathrm{~cm}$. The points $E, F, G$ and $H$ are the midpoints of the square's sides. Here, $E$ lies on $A B, F$ on $B C, G$ on $C D, H$ on $D A$.

a) Construct this square and connect the midpoints $E$ and $F, F$ and $G, G$ and $H$ as well as $H$ and $E$ with line segments!

b) Determine the area of the region $E F G H$!
b) The segments $E G$ and $F H$ divide the square $A B C D$ into four equal-area squares. Each of these squares is divided by the drawn diagonal into two (isosceles right) equal-area triangles.

The square $A B C D$ is composed of eight such triangles, and the area $E F G H$ is composed of four such triangles; its area is therefore half as large as that of $A B C D$. Since $14 \cdot 14=196$, the area of $A B C D$ is $196 \mathrm{~cm}^{2}$.

Since $196: 2=98$, the area of $E F G H$ is thus $98 \mathrm{~cm}^{2}$.