  In this study, we determine the mass radius of $^4$He, a very light nucleus,
by examining the near-threshold $\phi$-meson photoproduction data of the LEPS
Collaboration. To assess the gravitational form factor of $^4$He, we employ
multiple models for the mass distribution, including Yukawa-type, exponential,
Gaussian, and uniform functions. The mass radius of $^4$He is measured to be
$1.70\pm0.14$ fm, which is approximately equal to the charge radius of $^4$He.
Surprisingly, in contrast to the findings of the proton, no noticeable
discrepancy between the charge radius and the mass radius is noted for the
$^4$He nucleus. The proton and neutron distributions within $^4$He are likely
to be identical, confirming its regular tetrahedral structure in a new way. We
propose exploring the difference between charge and mass radii as a new
approach to examine the nuclear structure.
