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Byju's Answer
Standard VIII
Mathematics
Area of a Triangle
ABCD is a squ...
Question
ABCD is a square of area
153.76
c
m
2
. Find the area of the shaded part if P, Q, R, S are the midpoints of the sides.
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Solution
Area of the square
=
s
i
d
e
×
s
i
d
e
=
153.76
c
m
2
⇒
side = 12.4 cm
[Formula]
Area of the shaded region APQCRS = area of the square ABCD - area of the triangle PBQ - area of the triangle DSR
Area of the triangle
P
B
Q
=
1
2
×
(
6.20
×
6.20
)
=
19.22
c
m
2
[Since P and Q are the mid-points of the sides AB and BC]
Area of the triangle
D
S
R
=
1
2
×
(
6.20
×
6.20
)
=
19.22
c
m
2
[Since S and R are the mid-points of the sides AD and DC]
So, Area of the shaded region
=
153.76
−
19.22
−
19.22
=
115.32
c
m
2
[Substitute and simplify]
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In the figure, ABCD is a square whose sides are of length 2 cm. The midpoints of sides AB, BC, CD and DA are respectively P, Q, R and S. Four arcs are drawn with A, B, C and D as centres and AP as radius. Area of shaded portion is
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