  [Abridged] We compare H-alpha, ultraviolet (UV) and infrared (IR) indicators
of star formation rate (SFR) for a sample of z = 0.84 galaxies from the High-z
Emission Line Survey (HiZELS). Using multi-wavelength diagnostics, we estimate
that 5 - 11 per cent of H-alpha emitters at this redshift are active galactic
nuclei. We detect 35 per cent of the H-alpha emitters individually at 24
microns, and stack the star-forming emitters on deep 24-micron images in order
to calculate the typical SFRs of our galaxies. These are compared to the
observed H-alpha line fluxes in order to estimate the extinction at z = 0.84,
and we find a significant increase in dust extinction for galaxies with higher
SFRs. We demonstrate that the local relationship between SFR and extinction is
suitable for our sample, and attribute the overall increase in dust extinction
for z = 0.84 galaxies to an increase in the average SFR, rather than to a
change in dust properties. We calculate the UV extinction, and find a similar
dependence on SFR, but no evidence for a 2175 angstrom UV bump in the dust
attenuation law. We calculate the conversion between the dust attenuation of
nebular and stellar radiation, gamma, and show that gamma = 0.50 +/- 0.14. The
extinction / SFR relationship is shown to be applicable to galaxies with a
range of morphologies and bulge-to-disk ratios, to both merging and non-merging
galaxies, and to galaxies within high- and low-density environments, implying
that it is a fundamental property of star-forming regions. In order to allow
future studies to correct for a SFR-dependent amount of dust extinction, we
present an equation to predict the extinction of a galaxy, based solely upon
its observed H-alpha luminosity, and use this to recalculate the H-alpha
luminosity function and star formation rate density at z = 0.84.
