Tutors Answer Your Questions about Polygons (FREE)
Question 750879: 13/x+2 - 6/x squared + 2x
Answer by jim_thompson5910(28595)  (Show Source):
Question 750743: if polygons of n sides has 1/2n(n-3) diagonals, how many sides will a polygon with 65 diagonals have? is there a ploygon 80 diagonal
Answer by MathLover1(6632)  (Show Source):
You can put this solution on YOUR website!Let  be the number of sides = number of vertices.
Then   can be connected to  other vertices, giving  connections. However, this counts each vertex pair connection twice, so there are:
 diagonals.
Thus if there are  diagonals:
 ...write  as 
 ...group
so  or 
As a polygon cannot have a negative number of sides, .
if there are  diagonals:
 ...use quadratic formula
solutions:
so, since  and is equal to the number of sides, means that a polygon cannot have a number of sides as decimal number
there is  a polygon with diagonals
Question 749799: The interior angles of a regular polygon T measure 900. How many sides does t have?
Answer by Alan3354(30993)  (Show Source):
You can put this solution on YOUR website!The interior angles of a regular polygon T measure 900. How many sides does t have?
-----------
900/180 = 5
5 + 2 = 7
7 sides
=============
That would be true for irregular polygons also.
Question 749536: Each interior angle of a regular convex polygon measures 156°. How many sides does the polygon have?
Answer by Alan3354(30993) (Show Source):
You can put this solution on YOUR website!Each interior angle of a regular convex polygon measures 156°. How many sides does the polygon have?
------------
Exterior angles = 180 - 156 = 24 degs
360/24 = 15 sides
Question 747853: find the side length of a 15-sided regular polygon with apothem a=6 and area A= 282 square inches.
Answer by Alan3354(30993) (Show Source):
You can put this solution on YOUR website!find the side length of a 15-sided regular polygon with apothem a=6 and area A= 282 square inches.
----------------
Central angle = 360/15 = 24 degs
Each of the 15 segments can form 2 right triangles with the apothem and the side, and the angles at the center are 1/2 of 24 deg = 12 degs.
-----------
(s/2)/a = tan(12)
s = 2*a*tan(12)
s =~ 2.5507
Question 746810: if a polygon has 6 sides, find the sum of the interior angles
Answer by MathLover1(6632) (Show Source):
Question 746807: what is the measure of each interior angle of a 40 sided polygon
Answer by nerdybill(6958)  (Show Source):
You can put this solution on YOUR website!what is the measure of each interior angle of a 40 sided polygon
.
Interior Angle = 180° - 360°/n
Interior Angle = 180 - 360/40
Interior Angle = 180 - 9
Interior Angle = 171°
Question 746565: i have to find the area
Answer by solver91311(16885)  (Show Source):
You can put this solution on YOUR website!
The area of what? Oh! I'm supposed to guess! Well let me just get out my crystal ball and my swami turban... HEY! Wake up out there. Use your head for something besides a hat rack, please.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
Question 746507: Find the area of the polygon. All angles in the figure are right angles. Sides are 21ft 6ft 21ft 9ft 9ft and 15ft
Answer by Alan3354(30993) (Show Source):
You can put this solution on YOUR website!Find the area of the polygon. All angles in the figure are right angles. Sides are 21ft 6ft 21ft 9ft 9ft and 15ft
-------------
No figure is shown.
6 side lengths are given, I don't think all the angles can be 90 degs.
Question 746202: A convex polygon has 7 sides, what is the sum of interior angles
Answer by savvyhush23(50)  (Show Source):
You can put this solution on YOUR website!A convex polygon has 7 sides, what is the sum of interior angles.
.
.
The formula: 
where n - sides of the polygon
.
assuming that it is a regular polygon with sides are equal for the formula to be valid.
.
.
Therefore, 
Question 745953: Two polygons are similar with the longest side of one 8 and the longest side of the other 10. Find the ratio of the areas.
Answer by savvyhush23(50) (Show Source):
You can put this solution on YOUR website!Two polygons are similar with the longest side of one 8 and the longest side of the other 10. Find the ratio of the areas.
the area is the product or square of its side:
The ratio of sides is, 8:10 = 4:5
squaring it yields, 16:25
the ratio of the area is 16:25
Question 745698: I am having a brain freeze, I am 60 yrs old and working with some wood. I have a six sided light house . I need to replace the base boards . What is the exact angle I need to cut the wood .
Answer by Alan3354(30993) (Show Source):
You can put this solution on YOUR website!I am having a brain freeze, I am 60 yrs old and working with some wood. I have a six sided light house . I need to replace the base boards . What is the exact angle I need to cut the wood .
-----
The interior angles are 120 degrees, exterior 60 degrees.
Question 745457: In a regular polygon each interior angle is 140 degrees greater than each exterior angle. Calculate the number of sides of the polygon. How can i solve this?
Answer by savvyhush23(50) (Show Source):
You can put this solution on YOUR website!In a regular polygon each interior angle is 140 degrees greater than each exterior angle. Calculate the number of sides of the polygon. How can i solve this?
Let
i is the interior angle
e is the exterior angle
n is the number of sides
The formula:
 
 
"...interior angle is 140 degrees greater than each exterior angle..."
 
Substitute equation 1 and 2 to equation 3
Question 745052: The perimeter of a regular polygon is 48 and its apothem is 6.What is the area of the polygon?
Answer by savvyhush23(50) (Show Source):
You can put this solution on YOUR website!I hope you know what is the apothem of a regular polygon. If not just google it.
Ok, let us inscribed a circle in a regular polygon so that its radius is equal to the apothem.
The formula of Regular polygon Circumscribing a circle are:
 and 
In the perimeter formula, see that  , substitute it to the Area:
 where r = 6
Therefore, Area = 144 sq. unit.
Question 744957: The measures of an exterior angle of a regular n-gon is 72 degrees. classify the polygon by number of sides.
Answer by Alan3354(30993) (Show Source):
You can put this solution on YOUR website!The measures of an exterior angle of a regular n-gon is 72 degrees. classify the polygon by number of sides.
-------------
360/72 = 5 sides
Question 744948: So I have determined that by using Leonhard Euler's formula for polygon division
T(6) = 14
T(7) = 42 and
T(8) = 132
however I am confused about how T(n) changes when you ignore distinct vertices.
Could you explain how to find T(n) while ignoring said vertices.
Note: I'm not looking for the answer but rather an explanation on how to reach the answer.
Thanks!
Answer by rothauserc(208)  (Show Source):
You can put this solution on YOUR website!So Euler asked the following question
In how many ways can a plane convex polygon of n sides be divided into
triangles by diagonals?
and his formula is
En = 2*6*10***(4n-10) / (n-1)!
when dividing the polygon into triangles we, of course, ignore some distant vertices when we draw the diagonals......
Question 744396: its asking me to find the values of X and Y of the two similar polygons. i dont know how to do that can you help? the angles are : 60degress 18, 22, ydegress, 12, x+4
Answer by stanbon(57347) (Show Source):
You can put this solution on YOUR website!its asking me to find the values of X and Y of the two similar polygons. i dont know how to do that can you help? the angles are :
60degress 18, 22,
ydegress, 12, x+4
------
(x+4)/22 = 12/18
----
x+4 = 22(2/3)
x + 4 = 44/3
x = 44/3 - 12/3
x = 22/3
----------
Question: If you have a picture of the similar triangles,
are they right triangles?
==================================
Cheers,
Stan H.
-----
Question 741819: If a certain measurement of a polygon is 612 in2, it means:? Can I please have help solving this? I tried answering it but I can only think that it is squared.
Answer by fcabanski(874) (Show Source):
You can put this solution on YOUR website!Volume involves three dimensions, so it's in cubic units. Area involves two dimensions (for example l x w in a rectangle), so it's in square units.
 is in square units, so it's an area - surface area of a solid (like a cube or sphere) or area of a 2D figure (like a square or circle).
Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)
Question 741792: A circle is circumscribed about a regular nonagon. What is the measure of the arc between each pair of consecutive vertices? Round to nearest hundredth if necessary
Answer by josgarithmetic(1520) (Show Source):
Question 740789: a = 33, b = 11, c =
Found 2 solutions by Alan3354, lynnlo:
Answer by Alan3354(30993) (Show Source):
Answer by lynnlo(4164) (Show Source):
Question 740778: I have no clue as to how to answer this question! please help!
If the sum of the measures of the interior angles of a convex n-gon is equal to the sum of the measures of the exterior angles, how many sides does the n-gon have?
Found 2 solutions by Alan3354, lynnlo:
Answer by Alan3354(30993) (Show Source):
You can put this solution on YOUR website!If the sum of the measures of the interior angles of a convex n-gon is equal to the sum of the measures of the exterior angles, how many sides does the n-gon have?
----------------
The sum of exterior angles is always 360 degs, for all polygons.
--> what polygon has a sum of 360 degs for interior angles?
Answer by lynnlo(4164) (Show Source):
Question 740790: a = 5, b = 12, c = ____
Answer by lynnlo(4164) (Show Source):
Question 739768: So I have a parallelogram (the top is A B the bottom is D C) and angle A says (3x+10)andlge B says (8x+5) angle D says 5y. angle C says nothing. I was wondering how I am supposed to solve this when andlge D and B have diff letter names and nothing matches A. Thanks:)
Answer by rothauserc(208) (Show Source):
You can put this solution on YOUR website!we are given the parallelogram ABDC which means that AB is parallel to DC, furthermore opposite angles are equal which means
Angle A is equal to angle C and angle D is equal to angle B, also angles A and D add up to 180 degrees (supplementary angles) as well as angles B and C. So we have the following equations.
3x+10+5y=180
8x+5+angle C =180
but angle C = angle A so
8x+5+3x+10=180
11x+15=180
11x=165
x=15
substituting for x in equation one, we have
3*15 + 10 + 5y = 180
55 + 5y = 180
5y = 125
y = 25
so x = 15 and y = 25
that means angle A = 3 * 15 + 10 = 55, angel B = 8 * 15 + 5 = 125
angle D = 5 * 25 = 125 and angle C = angle A =55
Question 739054: For this exercise, consider a circle of radius 1, and corresponding inscribed and circumscribed polygons with the number of sides n = 3, 4, 5, 6, and 8.
For each n = 3, 4, 5, 6 & 8, what are the perimeters of the inscribed and circumscribed polygons with n sides?
Answer by KMST(1868)  (Show Source):
You can put this solution on YOUR website!NOTE:
I do not know what is expected of you because I do not know if this is homework for fifth grade, for college, or somewhere in between. I assume that using trigonometric functions is acceptable. I suspect that the intention is showing (by examples) how the perimeter approaches the circumference of a circle as the number of sides increases. (Note how  is always in between the perimeter for the inscribed and circumscribed polygons, an how both approach as the number of sides increases)
THE SOLUTION:
We can only solve the problem if those are regular (symmetrical) polygons, because otherwise the perimeter would change with the shape.
Connecting the vertices to the center, we can split a polygon with sides into congruent isosceles triangles. If we draw the altitudes, we split each isosceles triangle into two congruent right triangles, for a total of  right triangles.
  is the center of the circle and the polygon;  is the side of the polygon
The angles AOP and POB measure  (or  if you prefer degrees rather than radians)
FOR AN INSCRIBED POLYGON:
A and B are points on the circle and OA and OB are radii with length
The length of the side of the polygon is
and the perimeter is
FOR A CIRCUMSCRIBED POLYGON:
P is on the circle, OP is a radius with lenght 
The length of the side of the polygon is
and the perimeter is
Question 738463: if someone says the length is 40 what is a perminator of a hexagon
Answer by Alan3354(30993) (Show Source):
You can put this solution on YOUR website!if someone says the length is 40 what is a perminator of a hexagon
--------------
The length of what?
40 what?
-----------
What is "perminator?"
Question 736061: what is the difference between finding the sum of the interior angles of a polygon and finding the sum of the exterior angles of a polygon.
Answer by solver91311(16885) (Show Source):
You can put this solution on YOUR website!
The sum of the exterior angles of any polygon is 360 degrees. The sum of the interior angles of a polygon is a function of the number of sides (or angles, if you prefer -- same number either way).
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
Question 735774: how do i find the perimeter and are of the polygon 35m, 14m, 29m, 14m? and in the middle it has 8m?
Answer by Alan3354(30993) (Show Source):
You can put this solution on YOUR website!how do i find the perimeter and are of the polygon 35m, 14m, 29m, 14m? and in the middle it has 8m?
=================
not enough info
Question 735286: What is the length of one side of a regular pentagon if its perimeter is 20 cm?
Answer by Alan3354(30993) (Show Source):
You can put this solution on YOUR website!What is the length of one side of a regular pentagon if its perimeter is 20 cm?
-----------
Hint: a pentagon has 5 sides.
Hint #2: perimeter = the sum of the lengths of the sides
Hint #3: regular means they're the same length
Question 735266: The diagonal of a square is 56 centimeters long. Find the perimeter of the square to the nearest tenth.
Answer by lwsshak3(6505) (Show Source):
You can put this solution on YOUR website!The diagonal of a square is 56 centimeters long. Find the perimeter of the square to the nearest tenth.
***
let x=side of the square
The diagonal and two of the sides form a right triangle
By the pythagorean theorem, 
perimeter of the square=4x=158.4 cm
Question 735263: which statement is NOT true for all rectangles?
A. The diagonals are congruent and bisect each other.
B. Opposite sides are congruent and parallel.
C. The diagonals are perpendicular.
D.Opposite anglers are congruent.
Answer by solver91311(16885) (Show Source):
You can put this solution on YOUR website!
A and B are true. C is false unless the rectangle is a square. D is false because rectangles do not have fishermen. Had D been worded: "Opposite angles are congruent", then it would have been true.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
Question 735260: casey has a 13 inch television and a 52 inch television in her home. What is the ratio of the sizes of the smaller and larger tvs?
Answer by lynnlo(4164) (Show Source):
Question 733811: 3. If a hexagon has a radius (center to point of angle) of 6, what is the side of the hexagon?
Answer by jim_thompson5910(28595) (Show Source):
You can put this solution on YOUR website!Assuming this is a regular hexagon, the circum-radius is equal to the length of the side of the hexagon (since the hexagon breaks down into 6 congruent equilateral triangles). So the side is also 6 units.
Question 729701: what is the exterior angle of a Enneadecagon?
Answer by MathLover1(6632) (Show Source):
Question 729078: For the trapezoid shown, the ratio m
Answer by Alan3354(30993) (Show Source):
Question 728680: A regular pentagon and a regular hexagon share a vertex, as shown below.
What is the value of the angle measure (7x − 19)°, in degrees?
Answer by Alan3354(30993) (Show Source):
You can put this solution on YOUR website!A regular pentagon and a regular hexagon share a vertex, as shown below.
----
Nothing is shown below.
------
What is the value of the angle measure (7x − 19)°, in degrees?
Question 727836: regular hexagon ABCDEF with diagonal AC and exterior angle 1
Prove: m<2+m<3=m<1
**Note <2 is located at
I would place greater value on understanding the method rather than just the answer. Please help
Answer by KMST(1868) (Show Source):
You can put this solution on YOUR website! Hopefully exterior angle 1 is GCB. If side CD was extended in the other direction, I had to do more drawing, but the idea is the same.
The exterior angles of a polygon are the changes in direction as you move around along the perimeter. Going counterclockwise, you go from D to C, and change direction so that instead of continuing straight towards G, you head to B. The angle GCB is an exterior angle.
If you go around clockwise, you change direction at B, and instead of heading towards G, to go towards C. Angle GBC is an exterior angle too.
You can draw 2 exterior angles at each vertex.
Because a regular polygon is symmetrical, in an regular polygon all the exterior angles are congruent. That is why it does not matter which of the exterior angles was labeled as angle 1. They all have the same measure as GCB and GBC.
Angle GBC in supplementary to angle ABC, so
In triangle ABC, with BAC=2 and BCA=3,
 
The 2 equations together result in
   -->  
And since all exterior angles have the same measure,
   
Question 727547: how do you work out sides of regular pentagon
Answer by fcabanski(874) (Show Source):
Question 727538: Quadrilateral ABCD has vertices A( -6, -2 ), B( 0, -2), C( 4, 2), and D( 2, 6). What type of quadrilateral is ABCD? Explain your reasoning.
Answer by richwmiller(9135)  (Show Source):
You can put this solution on YOUR website!quadrilateral
edge lengths | (6 | 4 sqrt(2) | 2 sqrt(5) | 8 sqrt(2))~~(6 | 5.65685 | 4.47214 | 11.3137)
diagonal lengths | (2 sqrt(29) | 2 sqrt(17))~~(10.7703 | 8.24621)
area | 36
perimeter | 2 (3+6 sqrt(2)+sqrt(5))~~27.4427
interior angle sum | 360° = 2 pi rad~~6.283 rad
Question 726765: John is drawing a regular polygon. He has drawn two sides with an exterior angle measure of 45°, as shown below.
When John completes his regular polygon, what will be the sum, in degrees, of the measures of the interior angles?
Answer by Alan3354(30993) (Show Source):
You can put this solution on YOUR website!John is drawing a regular polygon. He has drawn two sides with an exterior angle measure of 45°, as shown below.
-------
Nothing is shown.
---------
When John completes his regular polygon, what will be the sum, in degrees, of the measures of the interior angles?
---
The sum of exterior angles of ALL polygons is 360 degrees.
360/45 --> 8 sides
Each interior angle = 180 - 45 = 135 degs
8*135 = 1080 degrees
Question 725819: How do i do
6X=5
9y-2x=7
Answer by Alan3354(30993) (Show Source):
Question 725369: A polygon has m sides. If one of its interior angles is 80 degrees, and the other interior angles are each equal to 160 degrees, find the value of m.
Answer by jim_thompson5910(28595) (Show Source):
You can put this solution on YOUR website!If there are m sides, then the angles sum up to 180(m-2) degrees
-------------------------------------------------------
There is 1 angle that is 80 degrees
There are m angles total, so this means that there are m-1 angles left (if one is already taken). These m-1 angles are all 160 degrees.
So
80 + 160(m-1) = 180(m-2)
Solve for m:
80+160(m-1)=180(m-2)
80+160m-160=180m-360
160m-80=180m-360
160m=180m-360+80
160m-180m=-360+80
-20m=-360+80
-20m=-280
m=(-280)/(-20)
m=14
So there are 14 sides (and 14 angles).
Question 725214: a square is inscribed in a circle if one side of the square measures 5cm what s the circumference of the circle
Answer by solver91311(16885) (Show Source):
Question 724694: consider a circle of radius 1, and corresponding inscribed and circumscribed polygons with the number of sides n = 3, 4, 5, 6, and 8.
Both perimeters tend toward a limiting value as n gets larger and larger. What number would this be?
Answer by solver91311(16885) (Show Source):
You can put this solution on YOUR website!
The circumference of the circle, which is to say 
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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