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  • Find the area of the shaded region in Figure, 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 (Use pi= 3.14).

Find the area of the shaded region in Figure, 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 (Use \pi = 3.14).

Answers (1)

Here ABCD is a square of side 12 cm.

Area of ABCD= (side)2=(12)2=144 cm2

Area of sector =\frac{\theta }{360^{\circ}} \times \pi r^{2}                                                                  here \theta=90^{\circ}

           

Here PSAP, PQBP, QRCQ, and RSDR all sectors are equal.

Area of 4 sectors =4 \times \frac{\theta }{360^{\circ}} \times \pi r^{2}

                                        =4 \times \frac{1 }{4} \times \pi r^{2}\\ =3.14 \times 36\\ =113.04 cm^{2}

Area of shaded region = Area of the square – Area of 4 sectors

                                     = 144-113.04

                                      =30.96 cm2

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