2026 AMC 10A Problem 17

For each edge of a regular hexagon with side length $1$ , a square is constructed inside the hexagon with that edge as one of its sides. The region interior to all six squares is the interior of a smaller hexagon, shown shaded in the figure below. The area of the smaller hexagon can be expressed in the form $\frac{a\sqrt{b}}{c} - d$ , where $a, b, c$ and $d$ are all positive integers, $a$ and $c$ are relatively prime, and $b$ is not divisible by the square of any prime. What is $a+b+c+d$ ?