# Areas _Heron's formula_ by andyikumar

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Areas (Heron's formula)

In mathematical geometry, Heron’s formula is used to calculate the area of triangle when the
length of all sides a triangle are given. With the help of herons formula we can easily find the
side of the triangle. So basically we can say that it is used in case of triangle. As we know that
a triangle is a closed figure that has three side and all sides are connected end to end with each
other. It has three interior angles, then sum of interior angles of a triangle is 180 degree. Let's
have a triangle whose sides are ‘a’, ‘b’, ‘c’ are given the length of the sides of a triangle, then
we will see how to solve heron's Formula.

he Heron’s formula is given as: Heron's formula = √ p (p – a) (p – b) (p – c); In the given
formula ‘p’ is given the half of the perimeter, then the perimeter of a triangle is given by:
Perimeter of a triangle = a +b + c / 2; here 'a', 'b', 'c' are the three sides of a triangle. Now we
will discuss how to find the area of triangle using heron’s formula: some steps are define to
find the area of triangle using heron's formula:

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Math.Edurite.com                                                         Page : 1/3
Step 1: First of all it is necessary to find all sides lengths of triangle To find the area of
triangle.
Step 2: If we have given all sides’ length of a triangle then first we find the perimeter of a
triangle.
Step 3: When we have all sides’ length and perimeter of a triangle then we can easily calculate
the area of triangle using the heron’s formula.
Suppose the three sides of a triangle is 12 inch, 13 inch and 15 inch. Then we have to calculate
the area of triangle by using heron’s formula. As we know that the heron’s formula is given
by:

Area of a triangle = √ p (p – a) (p – b) (p – c); we use all the above steps to find the area of
triangle. To find the area of triangle, first of all we have to find the perimeter of a triangle. so
the perimeter of a triangle is given by: Perimeter of a triangle = a +b + c / 2;
Perimeter = 12 + 13 + 15 / 2;
Perimeter = 40 / 2 = 20 inch. After finding the perimeter of a triangle, we have to put these
values in the heron's formula to get the area of triangle. On putting the perimeter values in the
heron's formula we get: heron formula is given by: heron's formula = √ p (p – a) (p – b) (p –
c);
Area of a triangle = √ 20 (8) (7) (5);
Area = √ 5600; on further solving we get:
so the area of triangle using heron's formula is 74.83 inch2.
This is how we can solve the Heron’s Formula and you can solve any problem of the same.
In geometry, a triangle has different types of properties which are:
Area – The area of triangle is given by:
area of triangle = 1 / 2 * b * h, here 'b' denotes the base and 'h' denotes the height of a triangle.