**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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