Geometry A Semester Exam
2022 please give full answer and not just letters
Question: What is the area of a triangle with sides of length 5, 6, and 7?
Answer: The area of a triangle with sides of length 5, 6, and 7 can be calculated using Heron's formula. Heron's formula states that the area of a triangle is equal to the square root of s(s-a)(s-b)(s-c), where s is half of the perimeter of the triangle and a, b, and c are the lengths of the sides of the triangle. In this case, s = (5 + 6 + 7)/2 = 9, so the area of the triangle is equal to the square root of 9(9-5)(9-6)(9-7) = sqrt(9*4*3*2) = sqrt(3456) = 58.77. Therefore, the area of the triangle with sides of length 5, 6, and 7 is 58.77.