## Areas in Rectangle

Given rectangle $ABCD$, find the ratio of the area of region $I$ to the area of region $II$.

Source: NCTM Mathematics Teacher

SOLUTION

Area of region $I=\frac{1}{2}\times base\times height$
$=\frac{1}{2}\times OA\times DH$
Area of region $II =\frac{1}{2}\times base\times height$
$=\frac{1}{2}\times OC\times DH$
Since the diagonals of a rectangle bisect each other, the area of region $I$ equals the area of region $II$ and their ratio equals $1$.

Answer: $1$.