  We present a faithful geometric picture for genuine tripartite entanglement
of discrete, continuous, and hybrid quantum systems. We first find that the
triangle relation $\mathcal{E}^\alpha_{i|jk}\leq
\mathcal{E}^\alpha_{j|ik}+\mathcal{E}^\alpha_{k|ij}$ holds for all subadditive
bipartite entanglement measure $\mathcal{E}$, all permutations under parties
$i, j, k$, all $\alpha \in [0, 1]$, and all pure tripartite states. It provides
a geometric interpretation that bipartition entanglement, measured by
$\mathcal{E}^\alpha$, corresponds to the side of a triangle, of which the area
with $\alpha \in (0, 1)$ is nonzero if and only if the underlying state is
genuinely entangled. Then, we rigorously prove the non-obtuse triangle area
with $0<\alpha\leq 1/2$ is a measure for genuine tripartite entanglement.
Useful lower and upper bounds for these measures are obtained, and
generalizations of our results are also presented. Finally, it is significantly
strengthened for qubits that, given a set of subadditive and non-additive
measures, some state is always found to violate the triangle relation for any
$\alpha>1$, and the triangle area is not a measure for any $\alpha>1/2$. Hence,
our results are expected to aid significant progress in studying both discrete
and continuous multipartite entanglement.
