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

The sides of a triangle are $4 \, cm, 5 \, cm$ and $6 \, cm$. The area of the triangle is equal to

The midpoints of the three sides of a triangle are $(1, 2)$,$(-1, 1)$,and $(0, 3)$. The area of this triangle is (in sq. units):

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 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 $OMN$?

If $D, E,$ and $F$ are the midpoints of the sides $AB, BC,$ and $CA$ of the triangle formed by the points $A\ (5, -1), B\ (-7, 6),$ and $C\ (1, 3)$ respectively,find the area of $\Delta DEF$.