13x27 using generic triangle

1. Break down the numbers using their place values:

13 = 10 + 3
27 = 20 + 7

2. Construct the multiplication grid (generic triangle method):

\begin{array}{c|c|c} & 20 & 7 \\\hline10 & 10 \times 20 & 10 \times 7 \\ & = 200 & = 70 \\\hline3 & 3 \times 20 & 3 \times 7 \\ & = 60 & = 21 \\\end{array}

3. Sum the individual products obtained in the grid:

200 + 70 + 60 + 21

4. Calculate the total sum:

200 + 70 = 270
270 + 60 = 330
330 + 21 = 351

Therefore, the final answer is:

351