Question

The given figure is made up of a square and two identical quadrants. Find the area of the part in the square excluding the quadrants

• A. $168c{m}^2$
• B. $336c{m}^2$
• C. $448c{m}^2$
• D. $3360c{m}^2$

Answer 1

The correct option is B $336c{m}^2$

Required shaded area $=2(ar△BCD-arBODE)$

Area of 1 quadrant $=\frac{\theta }{{360}^0}\times \pi r^2$

$=\frac{{90}^0}{{360}^0}\times \frac{22}{7}\times 28\times 28$

$=616$ ${cm}^2$

$ar△BCD=\frac{1}{2}\times 28\times 28=392{cm}^2$

$\therefore AreaBODE=616-392=224{cm}^2$

Now, required shaded area $=2(392-224)$

$=2\times 168=336{cm}^2$