## 227. Math Puzzle $4 / 84$

Given is the side length $a$ of the square $A B C D$. Around $B$ and $D$, circular arcs with radius $a$ are drawn. This creates an elliptical figure $E$ inside the square.

![](https://cdn.mathpix.com/cropped/2024_06_06_69be9c4355ed0dc2557cg-75.jpg?height=297&width=257&top_left_y=771&top_left_x=908)

1. What is the formula for calculating the area of the elliptical figure $E$?
2. What is the area of this figure $E$ if $a=3.5 \mathrm{~cm}$?
1. $E=\left(\frac{r^{2} \cdot \pi}{4}-\frac{r^{2}}{2}\right) \cdot 2$
2. $E=\left(\frac{3.5^{2} \cdot 3.14}{4}-\frac{3.5^{2}}{2}\right) \cdot 2=6.992 \approx 7.00 \mathrm{~cm}^{2}$