<prompt> Calculate the area of a triangle with the following sides: 10, 14, 8.  <response>: We can use Herons formula to calculate the area of the triangle. This formula states that the area of a triangle with sides of length a, b, and c, and s being the semiperimeter or half the perimeter, is given by the square root of ss-as-bs-c.First, lets calculate the semiperimeter, s:s a b c 2s 10 14 8 2s 16Now we can use the semiperimeter and the lengths of the sides of the triangle in Herons formula to find the area:Area ss-as-bs-cArea 1616-1016-1416-8Area 16628Area 1536Area 39.19 square units.Hence, the area of the triangle with sides of length 10, 14, and 8 is approximately 39.19 square units. 