TRIANGLE WORKSHEET SOLUTION 1

Find the area of the triangle formed by the points.

(i) (0, 0), (3, 0) and (0, 2)

Solution :

Let A(0, 0) , B(3, 0) and C(0, 2) be the vertices of the triangle taken in order.

x1 = 0          x2 = 3         x3 = 0

y1 = 0          y2 = 0         y3 = 2

Area of the triangle triangle ABC :

  =  (1/2)[(0 + 6 + 0) – (0 + 0 + 0)]

  =  (1/2)[6 - 0]

  =  (1/2)[6]

  =  3 square units

(ii) (5, 2) (3, -5) and (-5, -1)

Solution :

Let A (-5, -1), B (3, -5) and C (5, 2) be the vertices of the triangle taken in order.

x1 = -5          x2 = 3         x3 = 5

y1 = -1          y2 = -5         y3 = 2

Area of the triangle ABC :

  =  (1/2)[(25 + 6 - 5) – (-3 - 25 - 10)]

  =  (1/2)[(31 - 5) –(-38)]

  =  (1/2)[26 +38]

  =  (1/2)[64]

  =  32 square units

(iii) (-4, -5), (4, 5) and (-1, -6)

Solution :

Let A(-4, -5) , B(-1, -6) and C(4, 5) are the vertices of the triangle taken in order.

x1 = -4          x2 = -1         x3 = 4

y1 = -5          y2 = -6         y3 = 5

Area of the triangle ABC :

  =  (1/2)[(24 - 5 - 20) – (5 - 24 - 20)]

  =  (1/2)[(24 - 25) –(5 - 44)]

  =  (1/2)[(-1) – (-39)]

  =  (1/2)[-1 + 39]

  =  (1/2)[38]

  =  19 square units

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