Which formula calculates the area of a triangle using Heron's formula?

The area of a triangle can be calculated using Heron's formula, which is particularly useful when the lengths of all three sides are known. The formula is defined as follows:

Area = sqrt(s(s-a)(s-b)(s-c))

In this formula, 's' represents the semi-perimeter of the triangle, which is calculated as half the sum of the lengths of the sides. Specifically, s = (a + b + c) / 2, where 'a', 'b', and 'c' are the lengths of the triangle's sides.

Heron’s formula provides a way to find the area without needing the height of the triangle, making it valuable in scenarios where such height measurements might not be easily obtainable. The formula effectively accounts for the triangle’s dimension by incorporating all three sides and their relationships, allowing for accurate area calculation based on side lengths alone.

This is distinct from the other formulas provided. For instance, the formula involving base and height is specific to right triangles or requires the height for non-right triangles. The length times width formula applies to rectangles, and the area formula for a circle pertains only to circular shapes. Therefore, option B is the only one that correctly corresponds to Heron's formula for calculating the area