#### Answer

Difference in playing area = 4600 yd$^{2}$

#### Work Step by Step

First, find the area of the largest field.
Area of a rectangle: $A$ = $l$$w$
A$_{large}$ = (80 yd)(120 yd)
A$_{large}$ = 9600 yd$^{2}$
Second, find the area of the smallest field.
Area of a rectangle: $A$ = $l$$w$
A$_{small}$ = (50 yd)(100 yd)
A$_{small}$ = 5000 yd$^{2}$
Finally, to find the difference in playing room subtract the area of the smallest field from the area of the largest field.
Difference in area = $D$
$D$ = A$_{large}$ - A$_{small}$
$D$ = 9600 yd$^{2}$ - 5000 yd$^{2}$
$D$ = 4600 yd$^{2}$