Question

Question 11
Find the area of the shaded region in figure, where arcs drawn with centres, A, B , C and D intersect in pairs at mid - point P, Q, R and S of the sides AB , BC , CD and DA, respectively of a square ABCD (use $\pi =3.14$)

Answer 1

Given: Side of a square BC = 12 cm

Since, Q is a mid - point of BC.

$\therefore Radius=BQ=\frac{12}{2}=6cm$

Now, area of quadrant BPQ
$=\frac{\pi r^2}{4}=\frac{3.14\times (6{)}^2}{4}=\frac{113.04}{4}c{m}^2$

Area of four quadrants
$=\frac{4\times 113.04}{4}=113.04c{m}^2$

Now, area of square ABCD
$=(12{)}^2=144c{m}^2$

$\therefore$ Area of the shaded region = Area of square - Area of four quadrants

$=(144-113.04)=30.96c{m}^2$