Answer:
A 21,000-Btu unit that will cool 340 cubic meters;
Step-by-step explanation:
Calculating the volume of the five rooms, we have;
Room 1:
Volume = 2.4 *4*5
       = 48 m³
Room 2:
Volume = 2.4*4*4
       = 38.4 m³
Room 3:
Volume = 2.4*6*4
       =57.6 m³
Room 4:
Volume = 2.4*6*6
       =86.4 m³
Room 5:
Volume = 2.4*6*5.5
       = 79.2 m³
Total volume of the room = 48 +38.4 + 57.6 + 86.4 + 79.2
                      = 309.6 m³
From the total volume obtained above, the air condition that will be adequate to cool the house is  21,000-Btu unit since the obtained volume(309.6 m³) is within the range of the specify volume (340 cubic meters).