## Number of Square Units

What is the number of square units enclosed by the polygon $ABCDE$?
Source: NCTM Mathematics Teacher 2006

SOLUTION

Polygon $HEJC$ encloses polygon $ABCDE$.
Number of square units inside polygon $HEJC$
$9\times 10=90$
Number of square units inside polygon $GBC$
$6\div 2=3$
Number of square units inside polygon $HIBG$
$4$
Number of square units inside polygon $IAB$
$(4\times 4)\div 2=8$
Number of square units inside polygon $EJD$
$(5\times 10)\div 2=25$
Number of square units inside polygon $ABCDE$
$90-3-4-8-25=50$

Answer: $50$ square units