Area of Triangle

In this page area of triangle we are going to see the formula to find area of the shape triangle.

In the lower we have studied about how to find the area for any triangle. We will use the formula is (1/2 ) x base x height if the base and perpendicular height is given.But here we are going to see the another method that is if we are given the three vertices of a triangle we can find the area by using this formula.


Area of the triangle = 12 {x1(y2-y3) + x2(y3-y1) + x3(y1-y2)}

Here we are given three vertices. We need to consider those points as

(x1,y1) (x2,y2) (x3,y3)

Then we need to apply the appropriate values in the formula.Finally we get the area.Now we are going to see the example problems to this concept.

Example 1:

The vertices of a tri angle are (5,2) (-9,-3) and (-3,-5). Find the area

Solution:

Let A,B and C be the vertices of the given triangle

  A(5,2) B(-9,-3) and C(-3,-5)

Now we have

x1 = 5 , y1 = 2 , x2 = -9 , y2 = -3 , x3 = -3 , y3 = -5

Area of the triangle ABC = 1/2 {5(-3-(-5)) + (-9) (-5-2) + (-3) (2-(-3))}

                                =  1/2 {5 (-3+5)) + (-9) (-7) + (-3) (2+3))}

                                =  1/2 {5 (2) -9 (-7) -3 (5)}

                                =  1/2 {10 + 63 - 15}

                                =  1/2 { 73 - 15 }

                                =  1/2 {58}

                                =  29 Square Units.

Therefore the area of  ABC = 29 square units.

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Area of triangle to Analytical Geometry