1. **Problem Statement:** We have a square cardboard of side 80 cm. We cut out squares of side 10 cm from each corner to form an open box by folding the sides up. We want to find the dimensions of the base of the box after cutting and the height of the box. 2. **Formula and Explanation:** When squares of side $h$ are cut from each corner of a square of side $s$, the base of the resulting box will be a square of side $s - 2h$, and the height of the box will be $h$. 3. **Applying the values:** Here, $s = 80$ cm and $h = 10$ cm. 4. **Calculate the base side length:** $$ \text{Base side} = s - 2h = 80 - 2 \times 10 = 80 - 20 = 60 \text{ cm} $$ 5. **Height of the box:** $$ \text{Height} = h = 10 \text{ cm} $$ 6. **Summary:** After cutting and folding, the box has a base of $60$ cm by $60$ cm and a height of $10$ cm. 7. **Additional note:** This method is commonly used to create open boxes from flat sheets by cutting squares at the corners and folding up the sides. **Final answer:** Base dimensions: $60 \text{ cm} \times 60 \text{ cm}$, Height: $10 \text{ cm}$.