Question

Calculate the area of the shaded region common between two quadrants
of circles of radius 7 cm each (as shown in Figure​

Answer 1

Calculated Area is $\frac {256}{7}\ cm^2$

Step-by-step explanation:

• Area of the Shaded Region = Area of First Quadrant + Area of the second Quadrant - Area of Square

Now,

• Area of First Quadrant = $\frac {\theta}{360} \times \pi r^2$

= $\frac {90}{360} \times \frac {22}{7} \times 8^2$

= $\frac {1}{4} \times \frac {22}{7} \times 8 \times 8$

= $\frac {22}{7} \times 2 \times 8$

= $\frac {352}{7}\ cm^2$

• For Second Quadrant,

As radius & angle are same

• Area of second quadrant = Area of First Quadrant

= $\frac {352}{7}\ cm^2$

Now, Area of Square = Product of Both Sides

=  $8 \times 8$

= 64 $cm^2$

• Area of Shaded Region = Area of First Quadrant + Area of the second Quadrant - Area of Square

= $\frac {352}{7} + \frac {352}{7} - 64$

= $(\frac {352+352-64 \times 7}{7})$

= $\frac {704-448}{7}$

= $\frac {256}{7}\ cm^2$