Question

find the area of the shaded region. 5 cm 3 cm 7.63 cm² 6.3 cm² 5.63 cm² 3.5 cm²

Explanation:

Step1: Find the radius of the circle

The diagonal of the rectangle is the diameter of the circle. Given the diagonal is 5 cm, so the radius \( r = \frac{5}{2}= 2.5 \) cm.

Step2: Calculate the area of the circle

Using the formula for the area of a circle \( A_{circle}=\pi r^{2} \), substitute \( r = 2.5 \):
\( A_{circle}=\pi\times(2.5)^{2}=6.25\pi\approx 6.25\times 3.14 = 19.625 \) \( cm^{2} \)

Step3: Calculate the area of the rectangle

The rectangle has sides 3 cm and we can find the other side using Pythagoras (since diagonal is 5 cm). Let the other side be \( x \), then \( x=\sqrt{5^{2}-3^{2}}=\sqrt{25 - 9}=\sqrt{16} = 4 \) cm. So area of rectangle \( A_{rectangle}=3\times4 = 12 \) \( cm^{2} \)

Step4: Find the area of the shaded region

Shaded area = Area of circle - Area of rectangle: \( 19.625-12 = 7.625\approx7.63 \) \( cm^{2} \)

Answer:

\( 7.63\ cm^{2} \)