Find the area of the parallelogram with vertices k(1, 2, 2), l(1, 5, 3), m(3, 11, 3), and n(3, 8, 2).

On examining the sides of the parallelogram, we see that the side KL lies in the plane x=1, and the side MN lies in the plane x=3.

Hence the height of the parallelogram is h=(3-1)=2.

The length of side mKL=sqrt((5-2)^2+(3-2)^2)=sqrt(3^2+1^2)=sqrt(10)
The length of side mMN=sqrt((11-8)^2+(3-2)^2)=sqrt(3^2+1^2)=sqrt(10)

Therefore the area of the parallelogram is mKL*h = sqrt(10)*2 = 2sqrt(10)

Area of parallelogram =