Question

FIND THE AREA OF THE SHADED REGION IN FIGURE, WHERE ABCD IS A SQUARE OF SIDE 10CM. AND SEMICIRCLE ARE DRAWN WITH EACH SIDE OF THE SQUARE AS DIAMETER (USE π=3.14​

Answer 1

Given Figure :

$\setlength{\unitlength}{1.05 cm}}\begin{picture}(12,4)\thicklines\put(0,1){ . }</p><p>\put(1,1){\line(1,0){4}}\put(1,5){\line(1,0){4}}\put(1,1){\line(0,1){4}}\put(5,5){\line(0,-1){4}}\qbezier(3,3)(3.5,4.5)(5,5)\qbezier(3,3)(4.5,3.5)(5,5)\qbezier(3,3)(2.5,4.5)(1,5)\qbezier(3,3)(1.5,3.5)(1,5)\qbezier(3,3)(1.5,2.5)(1,1)\qbezier(3,3)(2.5,1.5)(1,1)\qbezier(3,3)(4.5,2.5)(5,1)\qbezier(3,3)(3.5,1.5)(5,1)\end{picture}$

Answer:

Area of shaded design is 57 cm².

Formula Use,

$\red \star \: \tt area \: of \: square ={ (sides) }^{2}$ \\ $\red \star \: \tt area \:of\: Semicircle = \frac{\pi {r}^{2}}{2}$ \\ $\red \star \: \tt area \:of \:circle = \pi {r}^{2}$

Calculation :

We have,

4 Semicircle given above figure 1.

so,

$\leadsto\tt \cancel4 \times \frac{ \pi {r}^{2} }{ \cancel2} \\ \leadsto \tt2 \times 3.14 \times 5 \times 5. \\ \leadsto \tt157\: {cm}^{2}.$

Now,

Area of Square

$\tt { (sides) }^{2} = 10 \times 10. \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tt = 100 \: {cm}^{2} .$

Required area find,

(Area of 4 Semicircle)-( Area of Square )

We get,

$\leadsto \tt157 - 100. \\ \tt\leadsto57 \: {cm}^{2} .$

Therefore, the required shaded design is 57 cm².