3. The two diagonals of a quadrilateral are perpendicular. The lengths of the diagonals are 14 and 30 . What is the area of the quadrilateral?
SolUTION
210

Label the quadrilateral $A B C D$ and let $A C=14$ and $B D=30$.
Let $M$ be the intersection of $A C$ and $B D$.
Let $A M=a, B M=b, C M=c$ and $D M=d$.
Then the sum of the areas is $\frac{1}{2} \times(a b+a d+c b+c d)=\frac{1}{2} \times(a+c) \times(b+d)=\frac{1}{2} \times 14 \times 30=210$.