The sector has a central angle of 270° and the radius is 9m. So, the area of the sector is:
A_sector = (270/360) * π * (9m)^2 = 57.15m²
To find the area of the triangle, we need to find the height of the triangle. We can use the Pythagorean theorem to find the height:
h = √[(9m)^2 - (4.5m)^2] = √(81m^2 - 20.25m^2) = √60.75m^2 = 7.8m
The base of the triangle is 4.5m (half of the diameter), so the area of the triangle is:
A_triangle = (1/2) * 4.5m * 7.8m = 17.55m²
Therefore, the area of the shaded segment is:
A_shaded segment = A_sector - A_triangle = 57.15m² - 17.55m² = 39.6m²
Rounded to the nearest tenth, the area of the shaded segment is 39.6m².