A pyramid has a square base of side length 10cm and a height of 15cm. What is the surface area of the pyramid?

Step 1 ：\(\text{Surface area of a pyramid} = \text{Base area} + \frac{1}{2}\times \text{Perimeter of base} \times\text{Slant height}\)

Step 2 ：\(\text{First, calculate the base area: } A_{base} = s^2 = 10^2 = 100cm^2\)

Step 3 ：\(\text{Next, calculate the slant height using the Pythagorean theorem: } s_{l} = \sqrt{h^2 + (\frac{s}{2})^2} = \sqrt{15^2 + (\frac{10}{2})^2} = \sqrt{225 + 25} = \sqrt{250} = 15.81cm\)

Step 4 ：\(\text{Finally, calculate the surface area: } A_{pyramid} = A_{base} + \frac{1}{2}\times \text{Perimeter of base} \times\text{s_{l}} = 100cm^2 + \frac{1}{2} \times 4 \times 10cm \times 15.81cm = 100cm^2 + 316.2cm^2\)