Heron was a Greek mathematician born around 10 AD who worked in applied mathematics and wrote extensively on mathematical and physical subjects. His geometrical works, written in three books, dealt largely with calculating the areas of different shapes, including deriving the famous formula for calculating the area of a triangle based on its three side lengths. This formula, known as Heron's formula, allows calculating the area of a scalene triangle using only the lengths of its three sides. The summary provides the key details that Heron was a Greek mathematician who made important contributions to geometry, in particular deriving the formula for calculating the area of a triangle from its three side lengths.

2. Heron, (also known as Hero) was a Greek
mathematician. He was born in about 10 AD
possibly in Egypt . He worked in applied
mathematics. His works in mathematics and
physical subjects are so numerous and varied that
he is considered to an encyclopedic writer in these
fields. His geometrical works deals largely with
problems on menstruation written in three books .
Book I deals with the area of square , rectangles ,
triangle , trapeziums , and various other
specialized quadrilaterals . Hero has derived the
famous formula of the area of triangle in terms of
its three sides..!

3. We have studied in earlier classes about figures
of different shapes such as squares , triangles ,
and quadrilaterals . We have also calculated
perimeters and the areas of some of these
figures like rectangles , squares etc.
We know that :
Area of triangle is :
½ * (base ) * (corresponding height)

4. Now suppose that we know the lengths of
the sides of a scalene triangle and not the
height. Can we still finds it’s area ?
YES WE CAN ! This formula was given by
HERON about the area of triangle and is
also known as HERON’S FORMULA:
And a , b , c are the sides of the
triangle.

5. Find the area of the triangle if its sides are 40 m , 24 m , and 32 m.
Let a : 24 m
let b: 32m
let c: 40 m
S = a+b+c / 2 = 24 +32 + 40/2
= 96/2 = 48.
Area of triangle : sq. root of s(s-a)(s-
b)(s-c)
= sq .root of 48(48-24)(48-32)(48-40)
= sq. root of 48 * 24* 16 * 8
= sq. root of 147456
= 384 sq. m