Area of Triangles · Hard problem

A rectangular room measures $10$ m by $8$ m. A triangular closet is partitioned off in one corner (base $3$ m, height $4$ m) and excluded from the livable area, while a triangular bay-window alcove (base $2$ m, height $5$ m) extends out from the room and is included in the livable area. What is the total livable area, in square meters?