Question

What is Heron's formula for the area of a triangle with sides of lengths a, b, and c, given the semi-perimeter s=(a+b+c)/(2)?

Answer 1

Heron's formula is used to find the area of a triangle using the lengths of its sides. The formula is A = √s(s - a)(s - b)(s - c), where s is the semi-perimeter and a, b, and c are the side lengths.

Step-by-step explanation:

Heron's formula is used to find the area of a triangle using the lengths of its sides. The formula is:

A = √s(s - a)(s - b)(s - c)

Where A is the area of the triangle, s is the semi-perimeter (s = (a + b + c)/2), and a, b, and c are the lengths of the sides of the triangle.

For example, if the lengths of the sides of a triangle are 5 cm, 7 cm, and 8 cm, the semi-perimeter would be (5 + 7 + 8)/2 = 10 cm. Plugging the values into Heron's formula, we get A = √10(10 - 5)(10 - 7)(10 - 8) = √10(5)(3)(2) = √300 = 17.32 cm^2.