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
Answers
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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