Question

What is the heroines formula? ​

Answer 1

Answer:

herons formula is used to find the area of triangle.

Step-by-step explanation:

formula = √s (s-a)(s-b)(s-c)

Answer 2

Answer:

Heron’s formula is one of the most important concepts used to find the area of a triangle when all the sides are known. Hero of Alexandra was a great mathematician who derived the formula for the calculation of the area of a triangle using the length of all three sides. It is also termed as Hero’s Formula. He also extended this idea to find the area of quadrilateral and also higher-order polygons. This formula has its huge applications in trigonometry such as proving the law of cosines or law of cotangents, etc.

Example: A triangle PQR has sides a=4, b=13 and c=15. Find the area of the triangle.

Semiperimeter of triangle PQR, s = (4+13+15)/2 = 32/2 = 16

By heron’s formula, we know;

A = √[s(s-a)(s-b)(s-c)

Hence, A = √[16(16-4)(16-13)(16-15) = √(16 x 12 x 3 x 1) = √576 = 24

This formula is applicable to all types of triangles. Now let us derive the area formula given by Heron.