  JWST has revealed a class of numerous, extremely compact sources, with
rest-frame red optical/near-infrared (NIR) and blue ultraviolet (UV) colours,
nicknamed "little red dots". We present one of the highest signal-to-noise
ratio JWST NIRSpec/PRISM spectra of a little red dot, J0647_1045 at $z = 4.5321
\pm 0.0001$, and examine its NIRCam morphology, to differentiate the origin of
the UV and optical/NIR emission, and elucidate the nature of the little red dot
phenomenon. J0647_1045 is unresolved ($r_e < 0.17$ kpc) in the three NIRCam
long-wavelength filters, but significantly extended ($r_e = 0.45 \pm 0.06$ kpc)
in the three short-wavelength filters, indicating a red compact source in a
blue star-forming galaxy. The spectral continuum shows a clear change in slope,
from blue in the optical/UV, to red in the restframe optical/NIR, consistent
with two distinct components, fit by power-laws with different attenuation:
$A_V = 0.54 \pm 0.01$ (UV) and $A_V = 5.7 \pm 0.2$ (optical/NIR). Fitting the
H$\alpha$ line requires both broad (full width at half-maximum $\sim 4300 \pm
300 km s^{-1}$) and narrow components, but none of the other emission lines,
including H$\beta$, show evidence of broadness. We calculate $A_V = 1.1 \pm
0.2$ from the Balmer decrement using narrow H$\alpha$ and H$\beta$, and $A_V >
4.1 \pm 0.2$ from broad H$\alpha$ and upper limit on broad H$\beta$, consistent
with the blue and red continuum attenuation respectively. Based on single-epoch
H$\alpha$ linewidth, the mass of the central black hole is $8 \pm 1 \times 10^8
M_\odot$. Our findings are consistent with a multi-component model, where the
optical/NIR and broad lines arise from a highly obscured, spatially unresolved
region, likely a relatively massive active galactic nucleus, while the less
obscured UV continuum and narrow lines arise, at least partly, from a small but
spatially resolved star-forming host galaxy.
