Question

Find the area of the shaded region in the square of side 7 cm as given in the figure.

• A. $36.5c{m}^2$
• B. $28c{m}^2$
• C. $11.5c{m}^2$
• D. $23c{m}^2$

Answer 1

The correct option is B $28c{m}^2$

Given that,
Side of the square = 7 cm
Diameter of the semicircle = 7 cm

We know that,
Area of the square = $(side{)}^2=a^2$
Area of the semicircle = $(\frac{1}{2}$)𝞹r${}^2$

Now,
Area of part I and part III
= Area of the square - Area of 2 semi circles
= $a^2-2\times \left(\frac{1}{2}\right)\times$ 𝞹r2
= 72 - 2 $\times$ (½) $\times$ (22/7) $\times$ (7/2)2
= 49 - 77/2
= $10.5c{m}^2$

Similarly, area of part II and part IV $=10.5c{m}^2$

Now, Area of shaded region
= Area of the square - area of the unshaded region
= Area of the square - Area of part I, II, III and IV
= 49 - 2 $\times$ 10.5
=$28c{m}^2$

Hence, area of shaded region is $28c{m}^2$.