Spectral lines in the extreme ultraviolet (EUV) observed on the Sun can originate either from the hot corona or the cooler chromosphere to corona transition region. In the present paper we concentrate on coronal lines and in particular on iron lines at 171, 195, and 284 angstrom, which have been frequently observed by the Solar and Heliospheric Observatory (SOHO)/Extreme Ultraviolet Imaging Telescope (EIT) and the Transition Region and Coronal Explorer (TRACE). The intensity of these lines emitted by the corona can be reduced by the presence of a cool gas, e. g., by prominence-like material, located in the corona. There are two mechanisms that can lead to a reduction of the line intensity: absorption and volume blocking. That part of the coronal radiation that comes from behind the cool gas can be partially absorbed. The main absorbers for the iron lines studied here are neutral hydrogen and neutral plus singly ionized helium. In this paper we calculate the optical thickness of their resonance continua at the wavelength positions of iron lines and compare it with that in the H alpha line center. The comparison of the derived values shows that they are quite similar. The second effect is due to the fact that cool structures in the corona do not emit any radiation in the EUV lines, which gives rise to an additional reduction of the observed intensity as compared with the surrounding corona-we have termed this "volume blocking.'' We further describe in this paper how these two effects can be used in a new way of performing prominence diagnostics. Our results are also applicable to other coronal lines detected by, e.g., the SOHO CDS or SUMER instruments.