Question

The area of the larger square is $a^2$ and that of the smaller square is $b^2$. Then find $\frac{\text{Area of the shaded portion}}{\text{Area of the larger square}}$

• A. $1-\frac{b^4}{a^4}$
• B. $1-\frac{b^2}{a^2}$
• C. $1-\frac{a^4}{b^4}$
• D. $1-\frac{a^2}{b^2}$

Answer 1

The correct option is B $1-\frac{b^2}{a^2}$

Area of a larger square $=a^2$

Area of a smaller square $=b^2$

Area of shaded region $=$ Area of a larger square $-$ Area of a smaller square

$=a^2-b^2$

$\therefore$ Area of shaded region $=a^2-b^2$

$\Rightarrow$ $\frac{Areaofshadedportion}{Areaoflargersquare}$ $=\frac{a^2-b^2}{a^2}=\frac{a^2}{a^2}-\frac{b^2}{a^2}=1-\frac{b^2}{a^2}$