find the area of a triangle formed by y=x , x=6 , y=0
Answers
The Eq. x=6 and y=x meet at (6,6).
Since x=6 is 6 unit away from center Base of triangle b=6.
Also x=6 meet y=x at (6,6) the pt. is 6 units above X-axis i.e Height of triangle h=6.
By area of triangle A =bh/2.
A=6*6/2=18 units sq.
Area of a triangle formed by y=x , x=6 , y=0 is 18 sq units
Given:
- A triangle formed by lines
- y=x
- x=6
- y=0
To Find:
- The area of a triangle formed
Solution:
Step 1 :
Find coordinates of triangles finding intersection of lines
y = x , x = 6
=> x = 6 , y = 6
(6 , 6)
y = x , y = 0
=> x = 0
( 0 , 0)
x = 6 , y = 0
(6 , 0)
Step 2 :
Formula for Area of triangle with coordinates (x₁ , y₁ ) , (x₂ , y₂) and (x₃ , y₃)
A = (1/2) |x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) |
Substitute the values (6 , 6) , ( 0 , 0) , ( 6 , 0)
A = (1/2) | 6(0 - 0) + 0(0 - 6) + 6(6 - 0) |
A = (1/2) | 0 + 0 + 36 |
A = (1/2) (36)
A = 18
Area of a triangle formed by y=x , x=6 , y=0 is 18 sq units
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