Mathematics
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Question 62
DF
+4
1
ABCD and EFGA are the squares of side 4 cm each.
In square ABCD, DMB and PMQ are the arcs of circles
with centres at A and C respectively. In square AEFG,
the shaded region is enclosed by two arcs of circles
with centres at A and Frespectively. What I is the ratio
of the shaded regions of the squares ABCD and AEFG
respectively.
D
P
G
M
E E
А
B
F
G
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Answer:
ABCD is square park divided into four equal square parks as shown in the adjoining figure. Semicircular flower beds are made as shown by the shaded region. Find the area of the shaded region.
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ANSWER
Side of square = 7m = Diameter of swmi-corcle.
∵ All four square are equal.
∴ Diameter are same for all semi-circle.
∴ Radius =
2
7
m.
∴ Area of one semi-circle =
2
π
(
2
7
)
2
=
7×2
22
×
4
7×7
m
2
∴ Area of four such semi-circle =4×
4
77
m
2
=
77 m
2
∴Area of shaded region =77 m
2
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