Required information

A metal machine component is mounted to the floor and wall as shown below. The mass of the machine component is $22$ kg $.$ This mass is uniformly distributed throughout the entire area of the component. It is desired to ultimately determine the reaction forces acting on the machine component at the two supports at A and $B$ by applying equilibrium to the component. However, before this can be done, the centroid of the machine component must be found in order to know where to apply the component's weight force.

Calculate the area of the overall machine component. $($Round the final answer to four decimal places.$)$