Question

the given figure shows a rectangle ABCD inscribed in a circle as shown alongside if ab equals to 28 cm and BC is equal to 21 cm find the area of the shaded portion of the given figure​

Answer 1

The area of the shaded portion of the given figure is 374.5$(cm^{2})$.

Step-by-step explanation:

1. Given data

 ABCD is a rectangle.

 AB=CD=28 (cm)

 BC= DA= 21 (cm)

2. Area of rectangle $=Length\times Breadth= 28\times 21=588 (cm^{2})$       ...1)

3.Diagonal of rectangle

  $AC =BD =\sqrt{Length^{2}+Breadth^{2}}$

  $AC =BD =\sqrt{28^{2}+21^{2}}$

  $AC =BD =\sqrt{1225}$

So

 AC = BD =35 (cm)

4. Where AC and BD are diameter(d) of circle.

   So

   Diameter of circle = d = 35 (cm)

5. Area of circle $=\frac{\pi \times d^{2}}{4}$

   Above equation can also be written as

   Area of circle$=\frac{22 \times d^{2}}{7\times 4}$

      Area of circle$=\frac{22 \times 35^{2}}{7\times 4}=962.5 (cm^{2}$  ...2)

6. So

  Area of shaded region = Area of circle -area of rectangle

   Area of shaded region = 962.5-588=374.5 $(cm^{2}$