Question

Squares ABCD and EFGH are congruent, AB$=10$cm and G is the centre of square ABCD. The area of the shaded region in the plane is ____________.

• A. $75c{m}^2$
• B. $100c{m}^2$
• C. $125c{m}^2$
• D. $175c{m}^2$

Answer 1

The correct option is A $75c{m}^2$

In $△ABG:$

height $h=\frac{1}{2}\left(AD\text{or}BC\right)=\frac{10}{2}=5cm$

area of $△ABG=\frac{1}{2}\times h\times AB=5\times 5=25c{m}^2$

Shaded area$=ar(sq.EFGH)-ar\left(△ABG\right)=(10\times 10)-25=75c{m}^2$