area of a sector of a circle is A = (centralangle/360)*pi*r²
so the area of the sector is
A = (90/360)*pi*6^2 = 9pi m²
area of the triangle is 1/2*b*h = 1/2*6*6 = 18 m²
area of shaded region is the area of the sector minus the area of triangle
so (9pi - 18) m² or approximately 10.274 m²