question_answer

Find the area of the shaded region in Fig. 2, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD of side 12 cm, [Use \[\pi =3.14\]]

Answer:

Given, ABCD is a square of side 12 cm. P, Q, R and S are the mid points of sides AB, BC, CD and AD respectively.

Area of shaded region

= Area of square \[-4\times \]Area of quadrant

\[={{a}^{2}}-4\times \frac{1}{4}\pi {{r}^{2}}\]

\[={{(12)}^{2}}-3.14\times {{(6)}^{2}}\]

\[=144-3.14\times 36\]

\[=144-113.04\]

\[=30.96\,\,c{{m}^{2}}\]