The area of the region ( x , y ) : 0 ≤ x ≤ 9 4 , 0 ≤ y ≤ 1 , x ≥ 3 y , x + y ≥ 2 is

Step-by-step solution

The region is a quadrilateral A B C D Now, area of the quadrilateral A B C D = area of triangle A B D + area of the triangle B C D So, area = 1 2 3 2 1 2 1 2 0 1 9 4 3 4 1 + 1 2 × 9 4 - 2 × 3 4 = 1 2 - 2 1 2 - 3 4 - 9 8 - 9 8 + 1 2 × 1 4 × 3 4 = 1 4 + 3 32 = 11 32