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15. Find the area of triangle whose vertices are (2, 3), (– 1, 0) and (2, – 4).​

Answer»

Answer :

  • AREA of the triangle is 10.5cm².

Given :

  • VERTICES of a triangle are (2 , 3), (-1 , 0), (2 , -4).

To Find :

  • Area of the triangle.

Solution :

Let

ABC be the triangle in which

  1. A = (2 , 3)
  2. B = (-1 , 0)
  3. C = (2 , -4)

Here

  • x1 = 2
  • x2 = -1
  • x3 = 2
  • y1 = 3
  • Y2 = 0
  • y3 = -4

As we know that

Area of a triangle is

  • ½ [x1 (y2 - y3) + x2 (y3 - y1) + x3 (y1 - y2)

Put the values in the formula

Now,

According to question :

→ 1/2 [ 2 {0 - (-4)} + (-1) {(-4) - 3} + 2 {3 - 0) ]

→ 1/2 [ 2 × 4 + (-1) × (-7) + 2 × 3 ]

→ 1/2 [ 8 + 7 + 6 ]

→ 1/2 × 21

→ 21/2

→ 10.5cm²

Hence, the area of the triangle is 10.5cm².



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