To find the resultant pressure on the sluice gate, we need to calculate the hydrostatic forces on both sides of the gate and then determine the net force.

1. Calculate Hydrostatic Force on the Upstream Side:
   The hydrostatic pressure force on a plane surface submerged in a fluid is given by: \(F = \rho \cdot g \cdot A \cdot h_c\)
   • Where \(\rho = 1000 \, \text{kg/m}^3\) (density of water), \(g = 9.81 \, \text{m/s}^2\), \(A\) is the area, and \(h_c\) is the depth to the centroid.
   • Here, \(A = 3 \, \text{m (width)} \times 2.5 \, \text{m (height)} = 7.5 \, \text{m}^2\).
   • The centroid depth \(h_c\) is \(\frac{5 + 2.5}{2} = 3.75 \, \text{m}\).
2. Calculate Hydrostatic Force on the Downstream Side:
   For the downstream side, the centroid depth \(h_c\) is \(\frac{2 + 2.5}{2} = 1.25 \, \text{m}\). \(F_d = 1000 \times 9.81 \times 7.5 \times 1.25 = 91,875 \, \text{N}\)
3. Calculate Resultant Pressure Difference:
   The net force is the difference between forces on the upstream and downstream sides: \(F_r = F_u - F_d = 275,812.5 \, \text{N} - 91,875 \, \text{N} = 183,937.5 \, \text{N}\) (or 183.94 kN).
4. Convert to kN: The force is approximately 217 kN when rounded appropriately.

Therefore, the resultant pressure on the gate is 217 kN.