Calculate the diameter of the tablecloth including the hem, and then calculate the area of the material.

The diameter of the table is $130 \text{ cm}$.
The additional length for the hem on each side is $25 \text{ cm}$.

The total diameter will be the table's diameter plus the hem allowance on both sides.

The diameter of the tablecloth is $\boxed{\text{1.8 m}}$.

24.2.2 Calculate the area (in m²) of the tablecloth material.
You may use the formula: $\text{Area} = \text{Side} \times \text{Side}$

The material size is $2.3 \text{ m}$. Assuming it's a square, the side length is $2.3 \text{ m}$.

The area of the tablecloth material is $\boxed{\text{5.29 m}^2}$.

24.2.3 Calculate the area (in m²) of the tablecloth that was cut from the material.
You may use the following formula: $\text{Area} = \pi (\text{radius})^2$, where $\pi = 3.142$

From 24.2.1, the diameter of the tablecloth is $1.8 \text{ m}$.

The area of the tablecloth is $\boxed{\text{2.54502 m}^2}$.

24.2.4 Calculate how much material was wasted when the table cloth was cut.
You may use the formula: $\text{Wasted material} = \text{Area of a material} - \text{Area of tablecloth}$

Area of material = $5.29 \text{ m}^2$
Area of tablecloth = $2.54502 \text{ m}^2$

The amount of material wasted is $\boxed{\text{2.74498 m}^2}$.