An open box is made by cutting the congruent squares from the corners of a rectangular sheet of cardboard of dimensions 20 cm $\times$ 15 cm. If the side of each square is 2 cm, the total outer surface area of the box is

### Concept & Surface Area of an Open Box When an open box is formed by cutting corners from a sheet and folding up the flaps, the outer surface area of the resulting box is exactly equal to the area of the original sheet minus the area of the cut-out pieces. Formula: $$ \text{Surface Area} = \text{Area of Sheet} - \text{Area of Cut Squares} $$ ### Step-by-Step Solution 1. **Given:** Dimensions of the rectangular cardboard sheet = 20 cm $\times$ 15 cm. Side of each cut square = 2 cm. 2. **Calculate Original Area:** The area of the entire rectangular sheet is $20 \times 15 = 300$ cm$^2$. 3. **Calculate Cut Area:** 4 squares are cut from the corners. The area of one square is $2 \times 2 = 4$ cm$^2$. The area of all 4 squares is $4 \times 4 = 16$ cm$^2$. 4. **Calculate Final Surface Area:** The remaining area forms the box, which is $300 - 16 = 284$ cm$^2$. ### Exam Strategy & Shortcut Instead of calculating the dimensions of the folded box ($16 \times 11 \times 2$) and applying the surface area formula $lb + 2(bh + hl)$, simply subtract the area of the removed squares from the total sheet area. It is conceptually identical and much faster. ### Common Pitfall Calculating the inner volume or needlessly calculating the final 3D box dimensions, which takes more time and introduces calculation errors. ### Final Answer Therefore, the correct answer is **284 cm$^2$**.