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2 answers:
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Answer:
Option E
Step-by-step explanation:
Central angles of a regular polygon =
Here, n = Number of sides of the regular polygon
Therefore, central angle of the regular polygon = = 45°
From the picture attached,
m∠AOB = = 22.5°
By tangent rule,
tan(∠AOB) =
tan(22.5°) =
AB = OB[tan(22.5°)]
AB = 5(0.414213)
= 2.07 in
Therefore, area of ΔAOC = 2 × (Area of ΔABO)
=
= AB × OB
= 2.07 × 5
= 10.35 in²
Since, area of the given regular octagon = 8 × (Area of ΔAOC)
= 8(10.35)
= 82.5 in²
Therefore, Option (E) is the answer.
Answer:
<em> = n² + 4n ; n = 11 </em>
Step-by-step explanation:
=
[2
+ (n - 1)d]
~~~~~~~~~
= 5
d = 7 - 5 = 2
=
[ 2(5) + 2(n - 1)] =
( 8 + 2n ) = 4n + n²
<em> = n² + 4n</em>
n² + 4n = 165
n² + 4n - 165 = 0
(n + 15)(n - 11) = 0 ( n ≥ 0 ) ⇒ <em>n = 11</em>