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  • 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 <img alt="\pi" src="https://entran

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]

 

 

 
 
 
 
 

Answers (1)

In ABCD square 

P,Q,R,S  are the midpoint of 

AB,BC , CD and DA 

AB = 12 cm 

AP  = 6cm = radius of each arc 

Area of one quadrant =

 \frac{1}{4} \pi r^2

Area of four-quadrant

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

Area of square ABCD  =

a^2 = 12 \times 12 = 144 cm ^2

Area of shaded region = Area of a square - Area of four-quadrant 

144 - 36 (3.14)= 30. 96 cm^2

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Safeer PP

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