1. **State the problem:** We need to find the length of segment $PH$ where $P$ is a vertex of the rectangular base PQRS and $H$ is the midpoint of the top edge $FG$ of the wedge. Given dimensions are $PQ=6$ cm, $QR=4$ cm, and $RG=2$ cm. 2. **Understand the geometry:** The base is rectangle PQRS with points: - $P=(0,0,0)$ as origin (assumed at bottom-left corner) - $Q=(6,0,0)$ along x-axis - $R=(6,4,0)$ along y-axis - $S=(0,4,0)$ Point $G$ is $2$ cm above $R$, so $G=(6,4,2)$. Point $F$ is above $S$, so $F=(0,4,2)$. 3. **Locate $H$, the midpoint of $FG$: ** $$H=\left(\frac{0+6}{2},\frac{4+4}{2},\frac{2+2}{2}\right)=(3,4,2)$$ 4. **Coordinates summary:** - $P=(0,0,0)$ - $H=(3,4,2)$ 5. **Calculate length $PH$: ** Using 3D distance formula: $$PH=\sqrt{(3-0)^2+(4-0)^2+(2-0)^2}=\sqrt{9+16+4}=\sqrt{29}$$ 6. **Answer:** $PH=\sqrt{29}$ which corresponds to option C.