Subjects geometry

Paper Area Pyramid

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Search Solutions

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.