As a mathematician help Opio prepare a sharing plan for piece of land.

The areas are given as $\sqrt{3200} \text{ m}^2$, $\sqrt{1800} \text{ m}^2$, and $\sqrt{9800} \text{ m}^2$.

$$A_1 = \sqrt{3200} \text{ m}^2 = \sqrt{1600 \times 2} \text{ m}^2 = 40\sqrt{2} \text{ m}^2$$ $$A_2 = \sqrt{1800} \text{ m}^2 = \sqrt{900 \times 2} \text{ m}^2 = 30\sqrt{2} \text{ m}^2$$ $$A_3 = \sqrt{9800} \text{ m}^2 = \sqrt{4900 \times 2} \text{ m}^2 = 70\sqrt{2} \text{ m}^2$$

The triangular plot has a base of $1500 \text{ m}$ and a height of $10 \text{ m}$.

$$A_4 = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 1500 \text{ m} \times 10 \text{ m} = 7500 \text{ m}^2$$

The total area is the sum of all four plots.

$$A_{\text{total}} = A_1 + A_2 + A_3 + A_4$$ $$A_{\text{total}} = 40\sqrt{2} \text{ m}^2 + 30\sqrt{2} \text{ m}^2 + 70\sqrt{2} \text{ m}^2 + 7500 \text{ m}^2$$ $$A_{\text{total}} = (40+30+70)\sqrt{2} \text{ m}^2 + 7500 \text{ m}^2$$ $$A_{\text{total}} = (140\sqrt{2} + 7500) \text{ m}^2$$

Using $\sqrt{2} \approx 1.41421$:

$$A_{\text{total}} \approx (140 \times 1.41421 + 7500) \text{ m}^2 \approx (197.9894 + 7500) \text{ m}^2 \approx 7697.99 \text{ m}^2$$

Opio wants to reserve $\frac{1}{2}$ of the total land for himself.

$$A_{\text{Opio}} = \frac{1}{2} \times A_{\text{total}} = \frac{1}{2} (140\sqrt{2} + 7500) \text{ m}^2$$ $$A_{\text{Opio}} = (70\sqrt{2} + 3750) \text{ m}^2$$ $$A_{\text{Opio}} \approx (70 \times 1.41421 + 3750) \text{ m}^2 \approx (98.9947 + 3750) \text{ m}^2 \approx 3848.99 \text{ m}^2$$

The remaining area is the other $\frac{1}{2}$ of the total land.

$$\text{Remaining area} = A_{\text{total}} - A_{\text{Opio}} = (140\sqrt{2} + 7500) - (70\sqrt{2} + 3750) \text{ m}^2$$ $$\text{Remaining area} = (70\sqrt{2} + 3750) \text{ m}^2$$ $$\text{Remaining area} \approx 3848.99 \text{ m}^2$$

The remaining area is to be distributed equally among Opio's 4 children.

$$A_{\text{each child}} = \frac{\text{Remaining area}}{4} = \frac{70\sqrt{2} + 3750}{4} \text{ m}^2$$ $$A_{\text{each child}} = \left(\frac{70\sqrt{2}}{4} + \frac{3750}{4}\right) \text{ m}^2$$ $$A_{\text{each child}} = \left(\frac{35\sqrt{2}}{2} + 937.5\right) \text{ m}^2$$ $$A_{\text{each child}} \approx \left(\frac{35 \times 1.41421}{2} + 937.5\right) \text{ m}^2 \approx \left(\frac{49.49735}{2} + 937.5\right) \text{ m}^2 \approx (24.7487 + 937.5) \text{ m}^2 \approx 962.25 \text{ m}^2$$

Sharing Plan for Opio's Land:

• Total consolidated land area: $\boxed{\left(140\sqrt{2} + 7500\right) \text{ m}^2 \approx 7697.99 \text{ m}^2}$
• Opio's reserved share: $\boxed{\left(70\sqrt{2} + 3750\right) \text{ m}^2 \approx 3848.99 \text{ m}^2}$
• Each of the 4 children's share: $\boxed{\left(\frac{35\sqrt{2}}{2} + 937.5\right) \text{ m}^2 \approx 962.25 \text{ m}^2}$