Question

Find the area of the shaded region.

• A. $29$ cm${}^2$
• B. $39$ cm${}^2$
• C. $49$ cm${}^2$

Answer 1

The correct option is B $39$ cm${}^2$


Area of the shaded region in given figure can be solved by two methods:

1. Adding the area of regions I, II, III and IV as depicted in below figure,
2. Subtracting the area of smaller square from the area of larger square.

The second method is more feasible.

And as we know,
Area of square $=$ Side $\times$ Side
$\therefore$ Area of bigger square $=8\times 8=64\text{cm}{}^2$

And area of smaller square $=5\times 5=25\text{cm}{}^2$

Therefore, area of shaded region $=64-25=39$ cm${}^2$

(b) is the correct option