In the figure below, OMPN is a square. If the area of the circle O is 4π then what is the area of the shaded region?
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Answer:
4 - π
Step-by-step explanation:
(a) Radius of circle
A = πr² Substitute value of A
4π = πr² Divide each side by π
r² = 4 Take the square root of each side
r = 2
(b) Area of MON
A = ¼ × area of circle
A = ¼ × 4π
A = π
(c) Area of MONP
l = r Substitute the value of r
l = 2
A = l² Substitute the value of l
A = 2²
A = 4
(d) Area of MPN
A(MPN) = A(MONP) – A(MON)
Area(MPN) = 4 - π