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UPSC CDS Math Quadrilateral and Polygon Questions
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© examsnet.com
Question : 3
Total: 41
The corners of a square of side ‘a’ are cut away so as to form a regular octagon. What is the side of the octagon ?
[2019 CDS-I]
a (
√
2
— 1)
a (
√
3
- 1 )
a
√
2
+
2
a
3
Validate
Solution:
Let x unit is cut from the corner of square of side a unit.
Side of octagon
=
√
x
2
+
x
2
=
x
√
2
x
+
x
√
2
+
x
=
a
⇒
x
=
a
2
+
√
2
Side of octagon
=
x
√
2
=
a
√
2
2
+
√
2
=
a
√
2
2
+
√
2
×
2
−
√
2
2
−
√
2
=
a
√
2
(
2
−
√
2
)
2
=
a
(
√
2
−
1
)
© examsnet.com
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