Triangle Worksheet Solution1





In this page triangle worksheet solution1 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) [6]

                                 = 3 square units

Therefore 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) [64]

                                         = 32 square units 

Therefore 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) [38]

                                 = 19 square units 

Therefore the area of  ABC = 19 square units.

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