Question

The figure shows a square with four quadrants. drawn at the corners to enclose a space. If the side
of squre = 14cm, then the area of the enclosed space is
14cm
a) 42cm
b) 36cm
c)44cm
d) 28cm

​

Answer 1

To find Area of Enclosed Region by all 4 Quadrants

Step-by-step explanation:

we need to find Area of A

As this is a square and radius are all equal

Hence region mentioned have equal areas

B = C = D = E

F = G = H = I

Point F if joined  with both bottom vertex of square  then its = 10

as its on arc of radius = 10

and hence form an equilateral triangle

so Area of A + D + E + H =  (60/360) π 14² + (60/360) π 14²  - (√3 / 4)14²

= 196 ( π/3 - √3 / 4)

Area of A + D + E + H  + C + G  =  (90/360) π 14² = 196 π/4

Area of C + G = 196 π/4 - 196 ( π/3 - √3 / 4)

= 196 ( √3 / 4  - π/12)

C+ G = D+H = E + I = B + F

=> B + C + D + E + F + G + H = 4 * 196 ( √3 / 4  - π/12) =  196 (√3  - π/3)

Area of A  =  Area of Square - Area of ( B + C + D + E + F + G + H)

= 14² - 196 (√3  - π/3)

= 196 ( π/3  + 1 - √3)

= 61.95 cm²

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