Question

Define Heron's first formulae in explaination?

Answer 1

Answer:

$s = \frac{a + b + c}{2} \\ \\ \sqrt{s(s - a)( s - b)(s - c)}$

Answer 2

Answer:

★ Heron's Formulae :

$\large\fbox{\sf Area\:of\:triangle = \sqrt{s(s - a) (s - b) (s - c)}}$

where a, b and c are the sides of triangle, and semi - perimeter (s) that is half the perimeter of the triangle = $\sf{\dfrac {a + b + c}{2}}$ (Refer to the attachment)

→ This method/formula is used where it is actually not possible to find the height of the triangle.

→ Heron's formula is used to find the area of the triangle where three lengths are already given.

→ It is discovered by Heron or Hero who was born in 10D (estimated) in Alexandria which is in Egypt.

→ This formula is also used to find the area of other polygons like, quadrilaterals.

Know more:

※ This question is taken from the book of grade 9th, chapter 12 (Heron's Formula).

※ The area of quadrilateral whose sides and one diagonal is given. Then, we can calculate it by dividing the quadrilateral into two triangles and also by using Heron's formula.

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