Question

In the given figure on a square handkerchief, nine circular designs each of the radius $7cm$ are made. Find the area of the remaining portion of the handkercheif

Answer 1

In given figure

$\square$ $AJLE$ $=\square$$ELMF$$=\square$ $FMNG$ $=\square$ $GNOH=\square HOPI=\square IPKB,$ are all squares
Also, $AE$$=$$EF$ $=$ $FG$ $=$ $GH$ $=$ $HI$$=$$IB$$=$ radius of circles $=7cm$
$\therefore$ $AB$ $=AE+EF+FG+GH+HI+IB$ $=42cm$
$\therefore$ Area of $\square ABCD$ $=42\times 42$
$=1764c{m}^2$
Area of $9$ circles $=9\pi \times r^2$$=9\times \frac{22}{7}\times 7\times 7$
$=1386c{m}^2$
$\therefore$ Area of remaining portion of the handkerchief $=1764-1386=378c{m}^2$