Question

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).

Answer 1

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)

Answer: Area of parallelogram = $2\sqrt{10}$