Question

Find the area in the first quadrant of the quadrilateral formed by the x-axis, the y-axis,

the line x= 2y−2 and the line y= 3−2x

Answer 1

Following is the quadrilateral formed by the x-axis, the y-axis, the line x= 2y−2 and the line y= 3−2x

We have divided quadrilateral into 3 parts two right triangle and one square:

Area of Quadrilateral = Area 1 + Area 2 + Area 3

Length of sides of square = 1, So, Area 2 = 1*1 = 1

Height of right triangle (Area 3) = 1

Base of right triangle (Area 3) = 0.5

So, Area 3 = 1/2*(1*0.5) = 0.25

Height of right triangle (Area 1) = sqrt((0-0.8)^2+(1-1.4)^2) = 0.8944

Base of right triangle (Area 1) = sqrt((1-0.8)^2+(1-1.4)^2) = 0.4472

So, Area 1 = 1/2*(0.8944*0.4472) = 0.20

Area of Quadrilateral = Area 1 + Area 2 + Area 3 = 1 + 0.25 + 0.2

Area of Quadrilateral = 1.45