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area of a triangle if you are given the boundary lines


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Find the area of the triangle formed by the lines
x+y=2, x-y=0,x+2y-6=0

first solve the equations of the lines taking them two
at a time to get the coordinates of the vertices of
the triangle
Use determinants or the formula for finding
the area of a triangle from coordinate geometry
to find the area of the triangle.
solving the first two equations
x+y = 2
x-y = 0 or x=y
substituting in the first equation
x+x=2
2x=2
x=1, y=1
point is A(1,1)

solving the second and third equation similarly we get
x=2 , y =2 and the point B(2,2)

solving the first and third equation using elimination
y = 4 and x=(-2 ) and the point  C(-2 , 4)

A(1,1) ,B(2,2), C(-2,4) are the vertices of the  triangle

use the formula to find the area of the triangle or determinants
or use the following matrix as guide multiplied with [1/2]
[ 1  2  -2 1 ]
[ 1  2  4  1 ]
 

area = [1/2]{ x1[y2-y3]+x2[y3-y1]+x3[y1-y2] }

area = [1/2]{[2+8+(-2)]-[2+(-4)+4]} =3sq. units

other questions and problems:


*integral calculus integration formula





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trigonometric identity and ratio of  certain standard angles

*list of differentiation formula     *integral calculus integration formula
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