Using integration, find the area of the region bounded by the lines, `4x-y+5=0; x+y-5=0\ \ ` and `x-4y+5=0`

Explanation

Solving the given equations in pairs , we get the points (A-1,1),B (0,5) and C (3,2)
Draw AL,BM and CN perpendiculars on the x-axis
Required area
`=underset(-1)overset(0)int"y AB dx" + underset(0)overset(3)int"y BC dx"-1/4.underset(-1)overset(3)int" y CA dx"`
`=underset(-1)overset(0)int(4x+5)dx + underset(0)overset(3)int(-x+5)dx-1/4.underset(-1)overset(3)int(x+5)dx `