Question

A rectangular sheet of paper ABCD is divided by 2 lines, each of which cuts its length and breadth into 2 equal parts respectively. Find the area of any one small rectangle.

• A. $\frac{1}{4}$ (Area of ABCD)
• B. $\frac{1}{8}$ (Area of ABCD)
• C. $\frac{1}{2}$ (Area of ABCD)
• D. None of these

Answer 1

The correct option is A $\frac{1}{4}$ (Area of ABCD)

Let $l$ be the length and $b$ be the breadth of rectangle.

We know that $Area=l\times b$

The first line cuts the length of the rectangle into half.

$\therefore$ The length becomes $\frac{l}{2}$. However the breadth is still the same.

Thus, $Are{a}_1=\frac{l}{2}\times b$

The second line cuts the breadth of the rectangle into half.

$\therefore$ The breadth becomes $\frac{b}{2}$. However the length remains $\frac{l}{2}$.

Thus, $Are{a}_2=\frac{l}{2}\times \frac{b}{2}$

$Area=\frac{l\times b}{4}$

$⟹Are{a}_2=\frac{1}{4}\left(AreaofABCD\right)$