Area of Triangles

Area of  Triangles

An Area of  triangle PQR with vertices  P(x1,y1), Q(x2,y2) , and R(x3,y3).

An Area of triangle PQR is denoted by ▲and is given as :

area of triangle

Note :

a) if an area of a triangle is given then use  ±  sign.

b) if points P, Q & R are collinear , then area of triangle is zero.

    1. Condition for three points to be collinear :

      If the area of triangle is zero  then all points must be collinear .

Types of Triangle :

1.Equilateral Triangle : all sides are equal

2.Isosceles Triangle : two sides are equal

3.Right-angled Triangle : two sides are perpendicular i.e one of them angle is 90°.

Stair method To calculate area :

In this method – 1st co-ordinates placed at first row and last row in determinant.

For right arrow use positive (+) sign and for left arrow use negative (-) sign.

  1. For Triangle 

In triangle PQR has vertices P(x1 , y1) , Q(x2 , y2 ) & R( x3 , y3 )


For Polygon:

The  area of polygon  with vertices are given as-

(x1 , y1 ) , (x2 , y2 ) , (x3 , y3 ) , … ,  (xn , yn ) .

stair method for polygon