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# Triangular Coordinate System

A packed figure which has three sides is known as triangle. Here we will see some properties of triangle. In a triangle the corner Point is known as the vertex of a triangle. In a triangle three vertices are present.
The distance measured around a triangle is known as perimeter of a triangle.
The sum of interior angles of a triangle is always 1800.
Now we will see Triangular coordinate system.
For finding the Area of Triangle when coordinates are given we need to follow some steps:
Step1: First we will find vertices of triangle.
Step2: For finding area, a formula is defined which is given below.
The formula is given below.
Area of triangle = |Fx (Gy – Fy) + Gx (Hy – Fy) + Hx (Fy – Gy)|,
2
Where ‘Fx’ and ‘Fy’ are the ‘x’ and ‘y’ of ‘F’ point.
Step 3: On putting values of all coordinates in formula we get area of triangle.
Suppose we have coordinates of a triangle P (3, 5), Q (5, 6) and R (10, 6), then by using these coordinates we find area of triangle.
For finding the area of triangle we need to follow above steps.
Here coordinates are F = (3, 5), G = (5, 6), H = (10, 6);
We know the formula for finding the area of triangle with vertices is given by:
Area of triangle = | Fx (Gy – Fy) + Gx (Hy – Fy) + Hx (Fy – Gy) |,
2
Now put the values in the given formula:
On putting the values we get:
Area of triangle = | 3 (6 – 5) + 5 (6 – 5) + 10 (5 – 6) |,
2
Area of triangle = | 3 (1) + 5 (1) + 10 (-1) |,
2
Area of triangle = | 3 + 5 + 10|,
2
Area of triangle = 18/2;
So the area of triangle is 9 inch2.

## Area of Triangle in Coordinate Geometry

Area of triangle in coordinate Geometry Coming Soon..

## Heron's Formula

Heron’s formula is used for calculating the Area of Triangle, it uses semi perimeter for calculation of area. Semi perimeter is given by:
S = ½ (p + q + r)
The area of the triangle by the heron s formula is given as: