1. **State the problem:** We need to find the total surface area of a closed box with a base of 15m by 15m and a height of 7.5m. 2. **Formula for total surface area of a closed rectangular box:** $$\text{Surface Area} = 2lw + 2lh + 2wh$$ where $l$ is length, $w$ is width, and $h$ is height. 3. **Identify the dimensions:** Length $l = 15$ m, Width $w = 15$ m, Height $h = 7.5$ m. 4. **Calculate each term:** - Base area (top and bottom): $2lw = 2 \times 15 \times 15 = 450$ - Side areas (length-height sides): $2lh = 2 \times 15 \times 7.5 = 225$ - Side areas (width-height sides): $2wh = 2 \times 15 \times 7.5 = 225$ 5. **Sum all areas:** $$\text{Total Surface Area} = 450 + 225 + 225 = 900 \text{ m}^2$$ 6. **Answer:** The total surface area of the box is $900$ square meters.