To determine the area of the triangular base of the prism, we first need to calculate the area of the triangle formed by the sides with lengths 6cm, 7cm, and 7cm.
First, to calculate the semi-perimeter of the triangle (s), we add the lengths of all three sides and divide by 2:
s = (6 + 7 + 7) / 2
s = 10
Next, we can calculate the area of the triangle using Heron's formula:
Area = β(s * (s - 6) * (s - 7) * (s - 7))
Area = β(10 * (10 - 6) * (10 - 7) * (10 - 7))
Area = β(10 * 4 * 3 * 3)
Area = β(360)
Area β 18.97 cm^2
Therefore, the area of the triangular base of the prism is approximately 18.97 square centimeters.