<prompt> Calculate the area of a triangle with sides of length 5, 7, and 10  <response>: To find the area of a triangle given the lengths of the sides, Herons formula can be used. Herons formula states that the area of a triangle is sqrtss-as-bs-c where a, b, and c are the side lengths of the triangle, and s is the semiperimeter of the triangle, calculated as a b c2.Using the values given for the side lengths of the triangle, a 5, b 7, and c 10. Thus, s a b c2 5 7 102 11.Substituting these values into Herons formula, we find the area of the triangle to be sqrtss-as-bs-c sqrt1111-511-711-10 sqrt11641 14.7.Therefore, the area of the triangle with sides of length 5, 7, and 10 is approximately 14.7 square units. 