Question

explain heron formula​

Answer 1

In geometry, Heron's formula (sometimes called Hero's formula), named after Hero of Alexandria, gives the area of a triangle when the length of all three sides are known. Unlike other triangle area formulae, there is no need to calculate angles or other distances in the triangle first.

Answer 2

Answer:

As per Heron's formula, the value of the area of any triangle having lengths, a, b, c, perimeter of the triangle, P, and semi-perimeter of the triangle as s is determined using the below-given formula:

Triangle with Given Side Lengths

Area of triangle ABC = √s(s-a)(s-b)(s-c), where s = Perimeter/2 = (a + b + c)/2

Example: Find the area of a triangle whose lengths are 5 units, 6 units, and 9 units respectively.

Solution: As we know, a = 5 units, b = 6 units and c = 9 units

Thus, Semi-perimeter, s = (a + b + c)/2 = (5 + 6 + 9)/2 = 10 units

Area of triangle = √(s(s-a)(s-b)(s-c)) = √(10(10-5)(10-6)(10-9))

⇒ Area of triangle = √(10 × 5 × 4 × 1) = √200 = 14.142 unit2

∴ The area of the triangle is 14.142 unit2