Question

The manager of and apartment complex will install new carpeting in a studio apartment. The floor plan is shown at the right. What is the total area that needs to be carpeted?\
help with 1 and 2 only

Answer 1

#1)
The area of the rectangular section in the middle is given by 15(12)=180ft².
The area to the right can be broken into a rectangle, whose area is 8(10)=80ft², and a triangle, whose area is (1/2)(5)(8)=20ft².
The area to the left can be represented as a rectangle minus a triangular area.  The dimensions of the complete rectangle would be 15(5)=75ft².  However it is missing a triangle at the top whose area would be (1/2)(5)(5)=12.5ft².  Thus we have 180+80+20+75-12.5=242.5ft².
#2)
The area of the weight room is given by 28(30)=840ft².  The area of the Dance Studio is given by 33(42)=1386.  There is a corner that is counted twice, however.  The area of this corner is 14(14)=196ft².  Our total area is then 840+1386-196=2030ft².