#### Answer

24$cm^{2}$

#### Work Step by Step

Given $A_{RSTV}$ = 48 $cm^{2}$
X is the midpoint of VT and Y is the midpoint of TS
Therefore VX = XT and TY=YS
Lets join RT
In triangle VRT, $A_{VRX}$ = $A_{VXT}$
In triangle RTS, $A_{RTY}$ = $A_{RYS}$
Because “A median of a triangle separates it into two triangles of equal area.”
$A_{RSTV}$ = $A_{VRX}$ + $A_{RXT}$ + $A_{RTY}$ + $A_{RYS}$
= $A_{RXT}$ + $A_{RXT}$ + $A_{RTY}$ + $A_{RTY}$
= 2 $A_{RXT}$ + 2 $A_{RTY}$
= 2($A_{RXT}$ + $A_{RTY}$)
= 2 $A_{RXTY}$
48 = 2 $A_{RXTY}$
$A_{RXTY}$ = $\frac{48}{2}$ = 24$cm^{2}$