23. Three congruent isosceles trapeziums are assembled to form an equilateral triangle with a hole in the middle, as shown in the diagram.

What is the perimeter of the hole?
A $3 a+6 b$
В $3 b-6 a$
C $6 b-3 a$
D $6 a+3 b$
E $6 a-3 b$
23. E Since the triangle formed when the trapeziums are put together is equilateral, the smaller angles in the isosceles trapeziums are both $60^{\circ}$. Consider one trapezium split into a parallelogram and a triangle as shown.

Since the original trapezium contains two base angles of $60^{\circ}$, the triangle also contains two base angles of $60^{\circ}$. Hence the triangle is equilateral and has side length $(b-a)$. Now consider the large equilateral triangle with the hole. The perimeter of the hole is $3(a-x)$ where $x$ is the length of the shortest sides of the trapezium. Therefore the perimeter of the hole is $3(a-(b-a))=3(2 a-b)=6 a-3 b$.