The area of the region enclosed by 4 |x| + 5 |y| ≤ 20 is

The four lines enclosing the given region are 4x + 5y = 20, 4x – 5y = 20, – 4x + 5y = 20 and – 4x – 5y = 20. Clearly, the four lines form a rhombus having diagonals of length 10 and 8.∴ Required area=12×10×8=40