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
49-x^2 factors to (7+x)(7-x). This is because both terms are perfect squares. When you divide out 7+x because a rectangle's area equals length times width, you get 7-x