Question 25
If the answer is not an integer, give the nearest integer. If the calculated answer has more than five digits, give its last five digits.
Let $ABCD$ be a square. Construct rectangle $ABEF$ with $E$ on segment $BC$ and $F$ on segment $AD$. Construct square $AGHF$ with $G$ on segment $AB$ and $H$ on segment $EF$. The areas of $ABEF$ and $AGHF$ are 42 and 18 respectively. Find the area of $ABCD$.
Let $ABCD$ be a square. Construct rectangle $ABEF$ with $E$ on segment $BC$ and $F$ on segment $AD$. Construct square $AGHF$ with $G$ on segment $AB$ and $H$ on segment $EF$. The areas of $ABEF$ and $AGHF$ are 42 and 18 respectively. Find the area of $ABCD$.