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Standard X
Mathematics
Trigonometric Ratios of Standard Angles
ABCD is a rec...
Question
ABCD is a rectangle such that
∠
C
A
B
=
60
°
and AC =
a
units. The area of rectangle ABCD is _______.
A
√
3
2
a
2
sq. units
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B
√
2
3
a
2
sq. units
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C
√
3
4
a
2
sq. units
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D
√
3
8
a
2
sq. units
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Solution
The correct option is
C
√
3
4
a
2
sq. units
In
△
A
B
C
, right angled at B
s
i
n
60
°
=
B
C
A
C
⇒
√
3
2
=
B
C
a
⇒
B
C
=
√
3
2
a
c
o
s
60
°
=
A
B
A
C
⇒
1
2
=
A
B
a
⇒
A
B
=
a
2
So, area of the rectangle
=
A
B
×
B
C
=
a
2
×
√
3
2
a
=
√
3
a
2
4
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