The diameter of the larger circle is 10.5 cm. the diameter of the smaller circle is 4.5 cm. what is the approximate area of the shaded region?

Area of the shaded region=area of the larger circle - area of the smaller cirlce.

1) we calculate the area of the larger circle.
diameter=10.5 cm
radius=diameter / 2=10.5 cm/2=5.25 cm
area=πr²=π(5.25 cm)²=27.5625π cm²

2) we calculate the area of the smaller circle:
diameter=4.5 cm
raduys=diameter / 2=4.5 cm/2=2.25 cm
area=πr²=π(2.25 cm)²=5.0625π cm²

3) we calculate the area of the shaded region.
area of the shaded region=27.5625π cm² - 5.0625π cm²=22.5π cm².
22.5π cm²=22.5(3.141592654...) cm²≈70.69 cm²

Answer : 22.5π cm²          or 70.69 cm²