Area of a rectangle having vertices A, B, C, D with position vectors $-\hat{i}+\frac{1}{2}\hat{j}+4\hat{k}, \hat{i}+\frac{1}{2}\hat{j}+4\hat{k}, \hat{i}-\frac{1}{2}\hat{j}+4\hat{k}$ and $-\hat{i}-\frac{1}{2}\hat{j}+4\hat{k}$ respectively is :

2

Vertices:

$A=(-1,\frac{1}{2},4),\ B=(1,\frac{1}{2},4),\ C=(1,-\frac{1}{2},4),\ D=(-1,-\frac{1}{2},4)$

Rectangle lies in the plane $z=4$.

Length $AB=|(1-(-1),\frac{1}{2}-\frac{1}{2},4-4)|=|(2,0,0)|=2$

Width $BC=|(1-1,-\frac{1}{2}-\frac{1}{2},4-4)|=|(0,-1,0)|=1$

Area $=AB \times BC=2\times1=2$

Required area = $2$