**Total Pressure on the Triangular Plane**

To calculate the total pressure on the vertical right-angled triangular plane immersed in water, we need to consider the pressure exerted at each point on the surface of the plane.

The pressure exerted by a fluid at a given point is determined by the depth of the point below the fluid surface and the density of the fluid. In this case, the fluid is water, which has a density of approximately 1000 kg/m³.

The total pressure on the plane can be calculated by integrating the pressure over the entire surface of the plane. However, since the plane is a right-angled triangle, we can simplify the calculation by dividing it into two smaller triangles.

**Pressure on the Vertical Face of the Triangle**

The vertical face of the triangle is a rectangle with a height of 2.4 m and a width of 2.0 m. The pressure on this face can be calculated by multiplying the depth of the centroid of the face below the water surface by the density of water and the acceleration due to gravity (9.81 m/s²).

The centroid of a rectangle lies at the center of the rectangle, so the depth of the centroid below the water surface is half of the height of the rectangle.

Depth of centroid = 2.4 m / 2 = 1.2 m

Pressure on the vertical face = Depth of centroid * Density of water * Acceleration due to gravity
= 1.2 m * 1000 kg/m³ * 9.81 m/s²

**Pressure on the Base of the Triangle**

The base of the triangle is also a rectangle with a length of 2.0 m and a width of 2.0 m. The pressure on this face can be calculated in a similar manner.

The centroid of a rectangle lies at the center of the rectangle, so the depth of the centroid below the water surface is half of the width of the rectangle.

Depth of centroid = 2.0 m / 2 = 1.0 m

Pressure on the base = Depth of centroid * Density of water * Acceleration due to gravity
= 1.0 m * 1000 kg/m³ * 9.81 m/s²

**Total Pressure**

The total pressure on the triangular plane is the sum of the pressures on the vertical face and the base.

Total pressure = Pressure on the vertical face + Pressure on the base

**Calculating the Centre of Pressure**

The center of pressure of a plane surface is the point at which the total pressure can be considered to act. It can be calculated using the moments of the pressure forces about a reference point.

To find the x-coordinate of the center of pressure, we need to calculate the moment of the pressure forces about the y-axis. Similarly, to find the y-coordinate, we need to calculate the moment of the pressure forces about the x-axis.

The moment of a force about an axis is equal to the force multiplied by the perpendicular distance of the force from the axis.

In this case, the pressure forces act perpendicular to the surface of the plane, so their moment arms are equal to their perpendicular distances from the axes.

The x-coordinate of the center of pressure can be calculated using the equation:

x-coordinate = (Moment of pressure on the vertical face + Moment of pressure on the base) / Total pressure

The y-coordinate of the center of pressure can be calculated using the equation: