  We conducted an optical monitoring survey of the Sagittarius dwarf irregular
galaxy (SagDIG) during the period of June 2016 -- October 2017, using the 2.5-m
Isaac Newton Telescope (INT) at La Palama. Our goal was to identify Long Period
Variable stars (LPVs), namely asymptotic giant branch stars (AGBs) and red
supergiant stars (RSGs), to obtain the Star Formation History (SFH) of
isolated, metal-poor SagDIG. For our purpose, we used a method that relies on
evaluating the relation between luminosity and the birth mass of these most
evolved stars. We found $27$ LPV candidates within two half-light radii of
SagDIG. $10$ LPV candidates were in common with previous studies, including one
very dusty AGB (x-AGB). By adopting the metallicity $Z = 0.0002$ for older
population and $Z=0.0004$ for younger ages, we estimated that the star
formation rate changes from $0.0005\pm0.0002$ M$_{\odot}$yr$^{-1}$kpc$^{-2}$
($13$ Gyr ago) to $0.0021 \pm 0.0010$ M$_{\odot}$yr$^{-1}$kpc$^{-2}$ ($0.06$
Gyr ago). Like many dwarf irregular galaxies, SagDIG has had continuous star
formation activity across its lifetime, though with different rates, and
experiences an enhancement of star formation since $z \simeq 1$. We also
evaluated the total stellar mass within two half-light radii of SagDIG for
three choices of metallicities. For metallicity $Z = 0.0002$ and $Z=0.0004$ we
estimated the stellar mass M$_*$ = ($5.4 \pm 2.3$) $\times$ $10^ 6$ and ($3.0
\pm 1.3$) $\times$ $10^ 6$ M$_{\odot}$, respectively. Additionally, we
determined a distance modulus $\mu$ = $25.27\pm0.05$ mag, using the tip of the
red giant branch (TRGB).
