1. **State the problem:** We need to find the total paper area required to make one hollow square pyramid tree, including the base.
2. **Given:**
- Side length of the square base, $s = 70$ cm
- Height of each triangular face (slant height), $h = 140$ cm
3. **Formula for area of the base:**
The base is a square, so its area is
$$\text{Area}_{base} = s^2$$
4. **Formula for area of one triangular face:**
Each triangular face has base $s$ and height $h$, so
$$\text{Area}_{triangle} = \frac{1}{2} \times s \times h$$
5. **Calculate the base area:**
$$\text{Area}_{base} = 70^2 = 4900 \text{ cm}^2$$
6. **Calculate the area of one triangle:**
$$\text{Area}_{triangle} = \frac{1}{2} \times 70 \times 140 = 35 \times 140 = 4900 \text{ cm}^2$$
7. **Calculate the total area of the four triangles:**
$$4 \times 4900 = 19600 \text{ cm}^2$$
8. **Calculate the total paper area needed:**
$$\text{Total area} = \text{Area}_{base} + 4 \times \text{Area}_{triangle} = 4900 + 19600 = 24500 \text{ cm}^2$$
**Final answer:** It will take $24500 \text{ cm}^2$ of paper to make each tree, including the bottom.
Paper Area Pyramid
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