Determine the coordinates of the centroid of the lines shown with respect to the indicated x and y axes

Determine the centroid ( x and y [this is x bar and y bar] ). If the centroid is at the line of symmetry, then state so.

A concrete gravity retaining wall has the section shown below: 0.3 m nies/201 2.1 m 1.2 m It retains sand weighing 14 kN/m³ with an angle of repose of 30°. The retaining wall weighs 24 kN/m³. The coefficient of base friction is 0.6. Calculate the safety factor against sliding.

For the given cross-sectional area: (1) Find the centroid and use it to calculate Ix , Iy and Ixy around the centroid axis (2) Based on Ix , Iy and Ixy in part (1), plot a Mohr’s circle and find Imax and Imin  (3) determine the Iu , Iv and Iuv with respect to new centroidal axes obtained by rotating the centroid axis, x, and y axes 45 degrees clockwise. Note: You must use the Mohr's circle to find Imax , Imin , and all parts of part (3)