In figure, if the midpoints of segments $\overline{GH}, \overline{JK}$, and $\overline{LM}$ are connected, calculate the area of the resulting triangle.

Midpoint of $GH$ is $\left (0, \dfrac {15}{4}\right)$

Midpoint of $JK$ is $(-5,-2)$

Midpoint of $ML$ is $(3,-2)$

If the coordinates of triangle is $(a,b) , (c,d) , (e,f)$ then the area formed by the coordinates of triangle is $\dfrac{1}{2} \times |a(d-f) + c(f-b) + e(b-d)|$

Therefore, the area enclosed by those midpoints will be

$\dfrac12 \times \left |0(-2+2) -5\left (-2-\dfrac {15}{4}\right) +3\left (\dfrac {15}{4}+2\right)\right|$

$= \dfrac {1}{2} \times |0+46|$

$= 23$