Question

The given figure is formed by 2 quarter circles and the area of the shaded square is 49 cm${}^2$. Find the perimeter of the figure. $(\text{Take}\pi =\frac{22}{7})$

• A. 94 cm
• B. 108 cm
• C. 86 cm
• D. 122 cm

Answer 1

The correct option is D 122 cm

Let us assume the side length of the square as $x$ cm.

Area of the square $=49$ cm${}^2$
$\Rightarrow x^2=49\Rightarrow x=7$
Therefore, the side length of the square is 7 cm.

The radius of the quarter circles $=14+x=14+7=21$ cm

Marking A, B, C, D, E, and F as the vertices of the given figure.
Perimeter of the figure = AB + Arc BC + CD + DE + Arc EF + FA
$=14+(\frac{1}{4}\times 2\times \frac{22}{7}\times 21)+14+14+(\frac{1}{4}\times \frac{22}{7}\times 21\times 21)+14$
$=56+33+33$
$=56+66$
$=122$ cm