## About "How to find area of triangle with 3 vertices"

How to find area of triangle with 3 vertices :

Here we are going to see how to find the area of triangle with given vertices.

To find the area of a triangle, the following steps may be useful.

(i) Plot the points in a rough diagram.

(ii) Take the vertices in counter clock-wise direction. Otherwise the formula gives a negative value.

(iii)  Use the formula given below

Let us look into some examples to understand the above concept.

Example 1 :

Find the area of triangle whose vertices are (6,7) (2,-9) and (-4,1).

Solution :

Now we have to take anticlockwise direction. So, we have to take the points in the order A (6, 7) C (-4, 1) and B (2, -9)

x₁ = 6     x₂ = -4      x₃ = 2

y₁ = 7     y₂ = 1       y₃ = -9

Area of the triangle ACB

=  (1/2) {(6 + 36 + 14) - (-28 + 2 - 54)}

=  (1/2) {56 - ( -82 + 2)}

=  (1/2) {56 - (-80) }

=  (1/2) {56 + 80)}

=  (1/2)  x 136

=  68 Square units.

Hence, the area of  ACB  =  68 square units.

Example 2 :

Find the area of triangle whose vertices are (3,4) (2,-1) and (4,-6).

Solution :

Now we have to take anticlockwise direction. So, we have to take the points in the order A (6,7) C (-4,1) and B (2,-9)

x₁ = 3     x₂ = 2         x₃ = 4

y₁ = 4     y₂ = -1        y₃ = -6

Area of the triangle ACB

=  (1/2) {(-3 - 12 + 16) - (8 - 4 - 18)}

=  (1/2) {(-15 + 16) - (8 - 22)}

=  (1/2) {1 - (-14) }

=  (1/2) x (1 + 14)

=  (1/2)  x 15

=  15/2  =  7.5 Square units.

Hence, the area of  ABC  =  7.5 square units.

Example 3 :

Find the area of triangle whose vertices are (5, 6) (2, 4) and (1, -3).

Solution :

Now we have to take anticlockwise direction. So we have to take the points in the order A (5, 6) B (2, 4) and C (1, -3)

x₁ = 5     x₂ = 2        x₃ = 1

y₁ = 6     y₂ = 4       y₃ = -3

Area of the triangle ABC

=  (1/2) {(20 - 6 + 6) - (12 + 4 - 15)}

=  (1/2) {20 - (16 - 15)}

=  (1/2) {20 - (1) }

=  (1/2) {20 - 1}

=  (1/2)  x 19

=  19/2  ==>  9.5 Square units.

Hence, the area of  ABC  =  9.5 square units.

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