The net in the picture is composed of identical isosceles triangles, each with an area of $2 \mathrm{~cm}^{2}$, and one of the internal angles of the triangle measures $100^{\circ}$. Determine the area and the size of the internal angles of the polygon depicted in this triangular net. (Note, the image may be very inaccurate.)

( $S$. Bednárová)

![](https://cdn.mathpix.com/cropped/2024_04_17_e148e2850cb5b4728907g-1.jpg?height=591&width=391&top_left_y=727&top_left_x=867)
One of the internal angles of the isosceles triangle measures $100^{\circ}$. It cannot be an angle at the base (otherwise, the sum of the internal angles would be greater than $200^{\circ}$). This means that the $100^{\circ}$ angle is at the main vertex, and the angles at the base are $40^{\circ}$. After filling in the angle sizes in the diagram, we get:

![](https://cdn.mathpix.com/cropped/2024_04_17_e148e2850cb5b4728907g-1.jpg?height=937&width=614&top_left_y=1602&top_left_x=755)

Area of the polygon: The given polygon can be divided into 12 whole triangles and 4 halves of these triangles. If each triangle in the grid has an area of $2 \mathrm{~cm}^{2}$, the area of the marked polygon is $12 \cdot 2 + 4 \cdot 1 = 28 \mathrm{~cm}^{2}$.