  We propose two semi-device-independent approaches that are able to quantify
unknown multipartite quantum entanglement experimentally, where the only
information that has to be known beforehand is quantum dimension, and the
concept that plays a key role is nondegenerate Bell inequalities. Specifically,
using the nondegeneracy of multipartite Bell inequalities, we obtain useful
information on the purity of target quantum state. Combined with an estimate of
the maximal overlap between the target state and pure product states and a
continuous property of the geometric measure of entanglement we shall prove,
the information on purity allows us to give a lower bound for this entanglement
measure. In addition, we show that a different combination of the above results
also converts to a lower bound for the relative entropy of entanglement. As a
demonstration, we apply our approach on 5-partite qubit systems with the MABK
inequality, and show that useful lower bounds for the geometric measure of
entanglement can be obtained if the Bell value is larger than 3.60, and those
for the relative entropy of entanglement can be given if the Bell value is
larger than 3.80, where the Tsirelson bound is 4.
