Derivation Of Heron’s Formula

1) Area of Triangles.

● Area of triangle using Heron's formula.

● Formula Derivation

DERIVATION OF HERON’S FORMULA :

Let 

We have a ∆ABC whose sides AB, BC CA are a, b & c in length respectively.

Construct  𝐴𝑃 ⊥ 𝐵𝐶 and mark it h.

If BP = d 

Then PC = BC – BP = (c – d)

We know that

Area of ∆ABC = ½ × Base × height

                         =  ½ × c × h  .........(1)

 

                                                   √3

Area of equilateral triangle = ____ (Side)²

                                                    4

                                                         √3

Area of equilateral triangle = 5 × ____ (Side)²

                                                          4

= 5 ×√3 × 

Area of an Irregular Polygon

To find the area of an irregular polygon you must first separate the shape into regular polygons, or plane shapes. You then use the regular polygon area formulas to find the area of each of those polygons. The last step is to add all those areas together to get the total area of the irregular polygon.

Let's look at some formulas for finding the area of polygons. Remember that:

b = base

h = height

a = length of a side

w = width

Area of a triangle = 1/2 x b x h

Area of a square = a2

Area of a rectangle = w x h

Area of a parallelogram = b x h

One can also calculate the area of any n-sided polygon using the formula:

Area = $n\ast s\ast a/2$

Where n is the number of sides, s is the length of a side, and a is called apothem.

The apothem is the length of a perpendicular line that connects the center of the polygon to any of its sides.

Area of n-sided polygon.