Find the area of the pentagon with vertices $A(1, 1)$,$B(7, 21)$,$C(7, -3)$,$D(12, 2)$,and $E(0, -3)$.

$OPQR$ is a square and point $Q$ is $(\alpha, \alpha)$. If $M$ and $N$ are the midpoints of sides $PQ$ and $QR$ respectively,then what is the ratio of the area of the square to the area of triangle $OMN$?

Find the area of a triangle given that midpoints of its sides are $(2, 7)$, $(1, 1)$, and $(10, 8)$.

The vertices of the triangle $ABC$ are $(2, 1)$,$(4, 3)$,and $(2, 5)$. If $D$,$E$,and $F$ are the mid-points of the sides,then the area of the triangle $DEF$ is:

$OPQR$ is a square and $M$ and $N$ are the midpoints of sides $PQ$ and $QR$ respectively. Then,the ratio of the area of the square to the area of the triangle $OMN$ is:

The area (in square units) of the triangle formed by the points with polar coordinates $(1, 0)$,$(2, \frac{\pi}{3})$,and $(3, \frac{2\pi}{3})$ is: