A pyramid has a slant height of $10 \mathrm{~cm}$ and a square base with area $64 \mathrm{~cm}^{2}$. What is the lateral area of the pyramid? $\mathrm{cm}^{2}$

Step 1 ：The lateral area of a pyramid is given by the formula \(\frac{1}{2} \times \text{perimeter of the base} \times \text{slant height}\).

Step 2 ：The base of the pyramid is a square, so the perimeter is \(4 \times \text{side length}\).

Step 3 ：The side length of the base can be found by taking the square root of the area, so \(\text{side length} = \sqrt{64} = 8.0\) cm.

Step 4 ：Then, the perimeter of the base is \(4 \times 8.0 = 32.0\) cm.

Step 5 ：Substitute the values into the formula, we get \(\frac{1}{2} \times 32.0 \times 10 = 160.0\) cm².

Step 6 ：Final Answer: The lateral area of the pyramid is \(\boxed{160 \mathrm{~cm}^{2}}\).