calculate the area of the trianglular region enclosed by the lines y=x+6, y=6-2x and y =-3

Question

_{calculate the area of the trianglular region enclosed by the lines y=x+6, y=6-2x}

_{and y =-3}

Answer 1

First we need to find where these three lines meet:

 

y = x+6 vs y = 6 - 2x:

               x + 6 = 6 - 2x

               0 = 6 - 2x - x- 6

               0 = -3x

               x = 0

They Intersect at (0,6)

 

y=x+6 vs y=-3:

              x+6 = -3

              x = -9

They intersect at (-9,-3)

 

y = 6 - 2x vs y = -3:

 6 - 2x = -3

 -2x = -9

  x = 9/2 = 4.5

They intersect at (4.5,-3)

 

The height is (0,6) to (0,-3) which is 9 units long

The base is (-9,3) to (4.5,-3) which is 13.5 units long

 

Area = 1/2*base*height = 1/2(13.5)(9) = 60.75