Let the sides of the rectangle be |AB|=|DC|=2x units, and |BC|=|AD|=2y units,
then
2x*2y = 72
4xy=74
xy=74/4=18. 5 (units squared)
The Area of rectangle:
ABCD= A(ABE)+A(ECF)+A(AFD)+A(AEF) (check the picture)
72 = A2+A3+A1+A(AEF)
[tex]72= \frac{1}{2} (2x)(y)+\frac{1}{2}(y)(x)+\frac{1}{2}(x)(2y)+A(AEF)[/tex]
[tex]72= xy+\frac{1}{2}xy+xy+A(AEF)[/tex]
[tex]72= 2.5xy+A(AEF)[/tex]
substituting xy=18.5:
72= 2.5*18.5+A(AEF)
72=46.25+A(AEF)
then, A(AEF)=72-46.25=25.75 (units squared)
Answer: 25.75 (units squared)
