To find the area of the shaded region, we need to subtract the area of the smaller semicircle from the area of the larger semicircle, and then subtract the area of the triangle.
First, we need to find the radii of the two semicircles. The larger semicircle has a diameter of 23.8, so its radius is 23.8/2 = 11.9. The smaller semicircle has a diameter of 15, so its radius is 15/2 = 7.5.
The area of the larger semicircle is (π/2)(11.9)^2 ≈ 222.93 square units.
The area of the smaller semicircle is (π/2)(7.5)^2 ≈ 44.18 square units.
Next, we need to find the area of the triangle. We can use the Pythagorean theorem to find the height of the triangle:
h^2 = 11.9^2 - 7.5^2
h^2 ≈ 72.16
h ≈ 8.49
The base of the triangle is 21, so the area of the triangle is (1/2)(21)(8.49) ≈ 89.29 square units.
Finally, we can find the area of the shaded region by subtracting the area of the smaller semicircle from the area of the larger semicircle, and then subtracting the area of the triangle:
222.93 - 44.18 - 89.29 ≈ 89.46
Therefore, the area of the shaded region is approximately 89.46 square units, rounded to the nearest hundredth.