Yahoo Answers: Answers and Comments for Finding angles and area in hexagon? [Mathematics]
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From Kitty
enUS
Fri, 16 May 2014 04:39:47 +0000
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Yahoo Answers: Answers and Comments for Finding angles and area in hexagon? [Mathematics]
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https://answers.yahoo.com/question/index?qid=20140516043947AAMH355
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From Vahucel: I created a formula to calculate the interior ...
https://answers.yahoo.com/question/index?qid=20140516043947AAMH355
https://answers.yahoo.com/question/index?qid=20140516043947AAMH355
Fri, 16 May 2014 13:00:30 +0000
I created a formula to calculate the interior angle of a regular hexagon
The formula is Angle = 180degrees  (360degress)/n where n is the number of sides....
Here if it has 4 sides the inteior angle is 180  360/4 = 180  90 =
90 degrees. OK! To confirm just graph the regular hexagon with 4 sides... it is a square... then the interior angle has 90 degrees OK!

From Viola: a) Exterior angle of a regular hexagon is 360/...
https://answers.yahoo.com/question/index?qid=20140516043947AAMH355
https://answers.yahoo.com/question/index?qid=20140516043947AAMH355
Fri, 16 May 2014 11:50:21 +0000
a) Exterior angle of a regular hexagon is 360/6 = 60°, so interior angle is 180  60 = 120°.
b) Because the hexagon is regular, the angle AOB must e 360/60 = 60°. Also by regularity, AO = BO, so AOB is isosceles. Therefore the other two angles are also 60°, so the triangle is equilateral.
c) Area of triangle is half base times height. Taking the base as 4 (units not given?), then imagine chopping such a triangle down the middle, making a rightangled triangle whose hypotenuse is 4 (one of the sloping sides), whose base is 2 (half the eq. triangle base), and whose perpendicular height is therefore, by Pythagoras' theorem, the square root of 4^2  2*2, which is 2 sqrt 3.
So the area of the eq. triangle is 0.5 * 4 * 2 sqrt 3, or 4 sqrt 3, approx. 6.928.
d) Since the hexagon is composed of six equal such eq. triangles, its area must be 24 sqrt 3, approx. 41.57.
e) PAB is a straight line, FAB is one of the interior angles of the hexagon therefore 120°, so PAF must be 180  120 or 60°.
f) PAF is one of those rightangled triangles described in (c). Therefore PA = 2 and PF = 2 sqrt 3. So the base of the rectangle in question is 2 + 4 + 2 = 8, and its height is 2 * 2 sqrt 3 = 4 * sqrt 3.
Therefore its area is the product of these numbers, i.e. 32 * sqrt 3, or approx. 55.43.