Question

A square tile of length 20 cm has four quarter circles at each corner as shown in below Fig. (1). Find the area of shaded portion. Another tile with same dimensions has a circle in the centre of the tile (see below Fig. (ii)]. If the circle touches all the four sides of the square tile, find the area of the shaded portion In which tile, area of shaded portion will be more? (Take = 3.14)​

Answer 1

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Answer 2

Answer(i). In (i) each one is a quarter circle. So, it is clear from the figure that radius of each quarter circle is r=10 cm

And area of square is 20 cm

So, Area of shaded portion = Area of square tile-4× Area of quarter circle =20×20−4× 4πr²

=400−4×3.14× 1/4×10×10

=400−314

=86cm 2

(ii).

In (ii) it is clear from the figure that diameter of the circle is 20 cmSo,

radius r = 220 =10 cm

So, Area of shaded portion = Area of square− Area of circle =20×20−πr²

=400−3.14×10×10

=400−314

=86cm²

Therefore, in both cases shaded region have equal areas.