Question

In the following figure, if the perimeter of the square is $20$, what is the area of the shaded region?

• A. $10$
• B. $12$
• C. $12.5$
• D. $20.5$
• E. $25$

Answer 1

The correct option is C $12.5$

Given perimeter $=20$
We know perimeter of a square is $4s$
$\therefore 4s=20$
$\therefore s=5$
Area $=s^2$
Area $=5^2=25$
Shaded portion comprises half of the square, so half of the area of square will be the area of shaded portion.
Area of shaded portion is $\frac{25}{2}=12.5$