# HOW TO FIND AREA OF TRIANGLE WHEN EQUATION OF SIDES ARE GIVEN

How to Find Area of Triangle When Equation of Sides are Given :

Here we are going to see an example problem to show how to find area of triangle when equation of sides are given.

## How to Find Area of Triangle When Equation of Sides are Given ?

Question 1 :

Find the area of a triangle formed by the lines 3x + y − 2 = 0 , 5x + 2y − 3 = 0 and 2x − y − 3 = 0

Solution :

3x + y − 2 = 0  ------(1)

5x + 2y − 3 = 0  ------(2)

2x − y − 3 = 0  ------(3)

Point of intersection of (1) and (2) is the vertex A

Point of intersection of (2) and (3) is the vertex B

Point of intersection of (3) and (1) is the vertex C

2(1) - (2)

6x + 2y - 4  =  0

5x + 2y - 3  =  0

(-)    (-)   (+)

-------------------

x - 1  =  0

x  =  1, By applying x = 1 in (1), we get

3(1) + y - 2  =  0

1 + y  =  0

y  =  -1

Vertex A(1, -1)

5x + 2y − 3 = 0  ------(2)

2x − y − 3 = 0  ------(3)

5x + 2y − 3 = 0

2(3) => 4x − 2y − 6 = 0

------------------

9x  =  9 ==> x  =  1

By applying x = 1 in (2), we get

5(1) + 2y - 3  =  0

2y + 2  =  0

2y  =  -2

y  =  -1

Vertex B (1, -1)

(1) + (3)

2x − y − 3 = 0

3x + y − 2 = 0

-----------------

5x - 5  =  0  ==> x  =  1

By applying x = 1 in (1), we get

2(1) - y - 3  =  0

-1 - y = 0

y  =  -1

Vertex C(1, -1)

A(1, -1) B(1, -1) and C(1, -1)

Now, let us find the area of triangle using the above vertices.  =  (1/2)[(-3 +3)]

=  0 square units. After having gone through the stuff given above, we hope that the students would have understood, "How to Find Area of Triangle When Equation of Sides are Given".

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