## TRIANGLE WORKSHEET SOLUTION1

Triangle worksheet solution1 :

Here we are going to see solution for each problems of the topic area of triangle worksheet.

(1) Find the are 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)are the vertices of the triangle taken in order.

x₁ = 0          x₂ = 3         x₃ = 0

y₁ = 0          y₂ = 0         y₃ = 2 Area of the triangle ABC

=  (1/2) [ (0 + 6 + 0) – (0 + 0 + 0)]

=  (1/2) [6 - 0]

=  (1/2) 

=  3 square units

Hence, the area of  ABC = 3 square units.

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

Solution:

Let A (-5, -1) , B (3, -5) and C (5, 2) are 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) 

=  32 square units

Hence, the area of ABC = 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) 

=  19 square units

Hence, the area of  ABC = 19 square units.

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