







A circle inscribed in a regular polygon 
20180712 

From Naveen: The radius of inscribed circle for n sided regular polygon of a side a is?
Please with proof Answered by Penny Nom. 





Needing the area of an irregular Pentagon 
20171206 

From Dale: I'm needing to find the square footage of an irregular pentagon.
I've seen the other questions similar to this one, but without a great deal of difficulty can't get you the angle degrees, or the length between opposing angles.
I'm hoping that a different bit of information can help. So here goes:
The longest side is 67ft long.
One of its legs is 39ft long, and the other is 18ft long.
The leg off of the other end of the 39ft leg is 35ft long.
The leg off of the other end of the 18ft is 49ft long, and meets the other end of the 35ft side.
The information that I DO have, which I'm hoping makes the difference, is that the 39ft and the 18ft sides are parallel.
Also, while the angles at each end of the 67ft side are not right angles, they are fairly close to it,
approximately 80 degrees at the 39 ft side corner, and 100 degrees at the 18ft side corner.
Dale. Answered by Harley Weston. 





An enclosure for some remote control boats 
20171003 

From Roberto: I am trying to build a "ring" for our remote control boats, using irrigation pipe.
I'd like to use full 20' long sticks for the long sides and use eight of what we call
45s, which are actually 135' fittings to make the six short sides. If I know the length
of the two long sides, what would be the formula to find the exact lengths of the short sides?
Thank you. Answered by Penny Nom. 





What is the regular price? 
20170511 

From Saira: If the sale price is 55.50$ and the discount is 12% what is the regular price Answered by Penny Nom. 





A regular tetrahedron 
20170312 

From Jeramie: When we have a regular tetrahedron, is it always true that all the angles of the triangles measure 60 degrees? Answered by Penny Nom. 





A barn roof 
20160529 

From Joe: Is it possible to build a barn roof (irregular pentagon?) with a 12' base and the other 4 sides 4' each? Thanks. Answered by Penny Nom. 





External and interior angles of a regular polygon 
20160419 

From pearl: a polygon has n sides.The exterior angle is 8 times the interior angle
find the value of the interior angle
find the value of n Answered by Penny Nom. 





The interior and external angles of a regular polygon 
20160217 

From percy: a regular polygon has n sides .The size of each interior angle is eight times the size of each exterior angle .
1.find the size of each exterior angle
2.calculate the value of n Answered by Penny Nom. 





A pentagon inscribed in a circle 
20150530 

From Victoria: find the area of a regular pentagon inscribed in a circle with radius 3 units Answered by Penny Nom. 





A hexagon with different side lengths 
20140516 

From Grace: Sorry if this is a simple question, but I can't seem to understand how to solve it. I am Trying to find the area of a hexagon with measurements 6x7x6x6x7x6, or 2 sets of opposing sides with 6, and one set with 7. Thank you. Answered by Penny Nom. 





The area of an irregular octagon 
20131118 

From zafar: if i have a rectangular octagon then how i can find its area
1. The length of rectangle is 42 and the width is 21 and and the base length is 4212 =30 i mean the
length of base =30 Answered by Penny Nom. 





Intersection points and diagonals 
20130911 

From Kenneth: I was wondering, is there a relationship between the number of sides of a regular ngon and the number of times its diagonals intersect?
Ie:
4 sides=1 intersect (center, diagonals form an 'X' )
5 sides=5 intersects (diagonals form a star)
6 sides=13 intersects
And so on. Answered by Chris Fisher. 





The fourth side of an irregular polygon 
20130201 

From Emran: I have a irregular polygon. I know 3 of the 4 sides, and 2 of the angles. AB is 285, BC is 149, and CD is 310. Angle B is 135 degrees. and Angle C is 45 degrees. Is there a formula to solve for the final side? Thanks. Answered by Penny Nom. 





An equilateral triangle and a regular hexagon in a circle 
20120911 

From Heidemarie: The vertices of an equilateral triangle with side length of 10 sqrt 3 cm lie on a circle. Find the side length of the regular hexagon whose vertices lie on the same circle. Answered by Penny Nom. 





The area of an irregular hexagon 
20120320 

From Jacob: I am having trouble finding the area of an irregular hexagon with 5 right angles.
It has 5 given sides, with the lengths as follows:
8.2 ft.
6 ft.
4.5 ft.
2.2 ft.
6 and one third ft. Answered by Chris Fisher. 





The volume of an irregular tetrahedron 
20120222 

From Brittany: If I am given an irregular tetrahedron with the coordinates of the 4 points how do I find the volume? For example I am asked to find the volume and only given the points A(4,3,5), B(2,1,2), C(0,5,0), and D(2,0,0) can you shown me the working and formular to find the volume? Answered by Robert Dawson. 





A regular hexagon inscribed in a circle 
20110718 

From Courtney: If ABCDEF is a regular hexagon inscribed in a circle of
radius r, prove that the length of each side of the hexagon
equals r. Answered by Penny Nom. 





Regular and irregular polygons 
20110310 

From thaera: the difference between regular shape and irregular shapes. Answered by Penny Nom. 





An irregular hexagon 
20110209 

From Emma: Hello,
I have math question about how to find the area of an irregular hexagon.
It is shaped like a backwards L and the side lengths are as follows
11cm
8cm
5cm
5cm
6 cm
3cm
Can you please help me find the area of this?
Emma Answered by Penny Nom. 





The area of a hexagon 
20100728 

From Katie: Hi i have to find the area of a hexagon with only the side length 2cm given
would you be able t help? Answered by Walter Whiteley. 





An irregular octagon 
20100309 

From Gayle: Question from Gayle:
I am building an irregular shaped octagon wooden box.
The measurements are 291/2 inches by 211/2 inches.
Sides are 12 inches.
It will be 36 inches high.
What would the cutting angles degrees be? Answered by Harley Weston. 





The inradius of an icosahedron 
20100121 

From fnavroth: Suppose you have an equilateral triangle.
The area of the triangle is exactly 1200 square centimetres.
Now suppose you have twenty of those triangles.
It's possible to assemble those twenty triangles into a closed
threedimensional shape, a regular polyhedron.
What would be the volume, in cubic centimetres, of the largest sphere
that could fit inside the shape? Answered by Chris Fisher. 





An irregular quadrilateral 
20091029 

From riya: what is irregular quadrilateral? Answered by Penny Nom. 





An area problem 
20090830 

From Amber: Area of hexagon ABCDEF with the vertices (3,0) (7,0) (9,2) (7,4) (3,4) (1,0) Answered by Harley Weston. 





Cubic yards in an Irregular Shape 
20090608 

From ron: hi i have a berm 100'w x200'L at the base and 9'tall the top is 85'L x 20'w i would to find out how many cubic yards are in the pile and the formula Answered by Janice Cotcher. 





Two regular hexagons 
20090421 

From niko: Two regular hexagons are ____________ similar. Answered by Stephen La Rocque. 





Surface area of an irregular shape 
20081215 

From Patrick: An irregular shaped object (lets say a gold nugget, not smooth with
pockets) can have its volume determined by comparing its mass in
water.
Is there any method or means or anything that could be used to
determine the surface area of this shape? Whether that be theoretical
mathematical formula to using a special infrared technique,etc...
The problem I foresee is that the component parts cannot be divided
into smaller geometric shapes. I would propose an answer although I
don't know if it is a good one: A liquid material that dries superthin, but
has a very specific and easily determined volume/mass is coated over
the object. Measure the mass difference between the beginning sample
of fluid and the mass after the object has been coated. Then determine
the surface area of the same mass of fluid in a geometric shape.
Is this feasible? Answered by Robert Dawson. 





A word problem about a regular pentagon 
20081116 

From Sandra: If the area of a regular pentagon is A=1.720a^2, in which a is one of the sides. Find the area of a regular pentagon with a side that measures 50cm. Answered by Chris Fisher and Penny Nom. 





An irregular, truncated pyramid 
20081024 

From phillip: Hi, I have a rectangular base to square top, pyramid shape to fabricate out
of steel plate (4 sections). The base is 3000mm by 800mm, the height is
1100mm and the top is 350mm square. What I need to know is the
lengths of the sides of the plate(were they meet vertically). Hope ive made
it clear enough. Thanks Phil. Answered by Stephen La Rocque. 





Irregular polygon and Circle that Intersects All Sides 
20080820 

From Xetro: Hi,
Suppose you have an irregular polygon(convex or concave) with n > 3 sides.
The question is  Find some circle that will cut(in limiting case  touch) all the sides of that polygon.
It doesnt matter how many times it cuts the side(1 or 2), it just have to cut or touch it.
How to find such a circle? or how to decide if such circle even exists?
What if those segments do not form a polygon but are some arbitrary segments ?
Really want to know how to do it................
Thanks a lot..
Regards,
Xetro Answered by Janice Cotcher. 





Angles in a regular tetrahedron 
20080807 

From Carla: Hi guys,
A regular tetrahedron has all its edges 8cm in length.
Find the angles which an edge makes with the base.
Thanks.
Carla Answered by Penny Nom. 





How do i find the area of an irregular figure? 
20080610 

From DAVE: How do i find the area of an irregular figure? Answered by Penny Nom. 





The area of a regular pentagon 
20080602 

From Jenna: I would like to know if there is a formula to find the area of a regular Pentagon that is not inscribed in a circle only apothem and side length are given. Answered by Penny Nom. 





The angles of an irregular pentagon 
20080520 

From victoria: The sum of the measure of two angles is 240. If the remaining angles are congruent, what is the measure of each angle? Answered by Penny Nom. 





An irregular tetrahedron 
20080424 

From RAUL: I am looking an expression for an edge length as function of the other five edge lengths of irregular tetrahedron. Answered by Walter Whiteley. 





A regular polygon 
20080409 

From chase: name the regular polygon if the sum of the measures of the polygon is 1,440 and the measure of one angle is 144 Answered by Stephen La Rocque. 





Side lengths and angles in a regular octagon 
20080409 

From Lori: I am a builder and need to find the length of the sides of an octagon. I know the length between
the parallel sides (26 feet). What is the length of each side? What is the angle measurement? Answered by Harley Weston. 





A fish tank in the shape of an irregular pentagon 
20080329 

From richie: i am building a fish tank. it is going to be an irregular pentagon. the sides are going to be
24"
24"
8"
8"
32"(approximately)
there will 3 right angles A, B, E
my question is how to figure out the degree of the angles that are not right angles (C,D)? Answered by Chris Fisher. 





A 6 pointed star 
20080304 

From Siddharth: When 2 congruent equilateral triangles share a common center, their union can be a star
If their overlap is a regular hexagon with an area of 60, what is the area of one of the original equilateral triangles?
a) 60 b) 70 c) 80 d)90 e)100 Answered by Stephen La Rocque. 





The centroid of a polygon 
20071229 

From David: I am playing around with an idea. I've read previous answers to questions
(using surveyor calculation methods) related to finding the area of an irregular
shape parcel of land (or irregular polygon). Is there a formula or method for
calculating the centroid (midpoint) for this type of polygon. I've seen plenty
of methods for calculating the midpoint for a triangle or regular shape poloygon
but few for an irregular shape polygon such as a parcel of land. Thanks... Answered by Harley Weston. 





An irregular octagon 
20071223 

From Sheldon: I am attempting to construct an irregular octagon picture frame out of bamboo. The bamboo is 1" in diameter and the opening should be 20" H X 16"W.
What measurements should be used? Answered by Penny Nom. 





Polygons 
20071209 

From Nicholle: a polygon with all sides the same length and all angles the same measure is called a  polygon.
What word goes in the blank. Answered by Penny Nom. 





The volume of a regular octagonal prism 
20071020 

From Chris: I am trying to figure out the volume of a regular octagonal prism, with side lengths of 4 inches. How do I do this? Answered by Penny Nom. 





Working with x 
20071012 

From Robert: The question: The measure of an exterior angle of a regular polygon is given. Find the measure of an interior angle, and find the sides.
41. 36 42. 18 44. 'X'
The attachment has what she has done for 41 and 42. Need help with 44 (lots of help) Thank you in advance for your site and your help. Robert Answered by Penny Nom. 





The perimeter of a regular polygon 
20070918 

From Ashwynn: why does the area of regular polygons with a perimeter of 1000m increase as the number of sides increase? Answered by Stephen La Rocque. 





An irregular lot 
20070912 

From Jay: How do I calculate the area of the following Lot?
N 15 degrees 1 minute 22 seconds E for 182.2 feet
S 89 degrees 46 minutes 26 seconds E for 218.4 feet
N 51 degrees 16 minutes 21 seconds E for for 307.1 feet
L= 31.63 feet with a radius of 50 feet
There is a discrepancy between county records and what the landowner is telling me Answered by Stephen la rocque and Harley Weston. 





Is there a way I can calculate correct square footage for odd shapes? 
20070831 

From Tom: I manage a golf course, and we are about to over seed the course for the upcoming winter months. We will be over seeding all greens, fairways, and tee boxes. Noone of the area that we will be placing seed on is a regular shape. The closest shapes they would be is a circle, rectangle or square, but most of them are all odd CURVED shapes. I know what the equation is for Square ft., and I know how many Square ft. are in an acre, but I need to be precise with the amount of seed I order. Is there a way I can calculate correct square footage for odd shapes. Answered by Harley Weston. 





All five angles of a pentagon ABCDE are equal 
20070804 

From Jerry: All five angles of a pentagon ABCDE are equal. The diagonals AC, AD and BD have the same length. Prove that all five sides of the pentagon are equal in length. Answered by Penny Nom. 





An irregular hexagon 
20070703 

From Rebecca: I need to find the shape of an irregular hexagon, but only have the lengths four of the sides.
It actually looks like a rectangle with a trapezoid on top of it.
The bottom of the rectangle is 150'. The sides are 75'. The length of the top is 130'. I do not have the lengths
of the two smaller sides.
Is there any way to find the area of this shape? Answered by Penny Nom. 





The area of an irregular polygon 
20070627 

From chris: finding square footage of a polygon with unequal measurements Answered by Stephen La Rocque and Harley Weston. 





What is the name of the shape that is 3D and irregular? 
20070614 

From alan: What is the name of the shape that is 3D and irregular? Answered by Stephen La Rocque and Penny Nom. 





Discovering the incircle of an irregular polygon 
20070525 

From Joaquim: I've been searching in some books and many websites, but I couldn't find a formula or algorithm for discovering the incircle of an irregular polygon, could you please help me? Answered by Walter Whiteley. 





The area of a regular octagon 
20070417 

From Adam: I need to find the area of a regular octagon with side length of 12.5m Answered by Penny Nom. 





The area of a regular hexagon 
20070414 

From Chantel: Could you please explain to me why the formula for a regular hexagon is
3√3/2 multiplied by side²? Thank you very much. Answered by Stephen La Rocque. 





The area of an irregular pentagon 
20070414 

From Steven: I have been given a coursework in which i have to investigate various shapes to find the one that would give the largest area with 1000m perimeter.
I'm stuck in a part where i have to calculate the area of a irregular pentagon. i don't know where to start from. I can make up the length of all the sides (5 sides), so long they add up to 1000, but i'm not quite sure what to do after that. Answered by Penny Nom. 





Interior and exterior angles 
20070402 

From Anuj: If in a regular polygon, each exterior angle is twice the interior angle,find the number of sides? Answered by Leeanne Boehm. 





The area of an irregular pentagon 
20070326 

From grace: hi I am doing graphics and need to find the area of the section given to us (it is just drawn). the sides measure 15m, 35.4m, 5m, 17.8m, 35.7m. the angle between the 15m side and the 35.4m side is 17degrees, the angle between the 35.4m side and the 5m side is 73degrees. the angle between the 5m side and the 17.8m side is 151degrees, the angle between the 17.8m side and the 35.7m side is 90degrees and the angle between the 35.7m side and the 15m side is 95degrees. if you could tell me the area i would be extremely grateful. thanks very much. Answered by Penny Nom. 





A regular quadrilateral 
20070313 

From Jackie: How can the measure of each angle of a regular quadrilateral be determined? Answered by Haley Ess. 





An irregular pentagon 
20070308 

From kelly: If I have a pentagon with 2 sides of length 5 and one with a length of 2, what are the lengths of other 2 sides? Answered by Stephen La Rocque. 





An irregular polygon 
20070306 

From Dike: How do i construct an irregular polygon Answered by Penny Nom. 





The altitude of regular nside pyramid 
20070126 

From Wendimu: The altitude of regular nside pyramid is half of it's base side.What is the angle between the lateral face and it's base? Answered by Penny Nom. 





A regular pentagonal pyramid 
20070125 

From Vickifazio: a regular pentagonal pyramid has a base perimeter of 1,085 ft. How long is one side of the base? Answered by Stephen La Rocque. 





Irregular multi sided polygon 
20070120 

From Graham: I have an irregular polygon. I know the length of all the sides and know approximately all the internal angles. Is there a formula or table that can calculate the area for me? Answered by Steve La Rocque, Chris Fisher and Penny Nom. 





The area of an irregular pentagon 
20070118 

From Ranjit: I would like to find the area of an irregular pentagon where the total perimeter is 1000m. Is there a Heron's formula for this? Answered by Stephen La Rocque. 





A regular polygon inscribed in a circle 
20061219 

From Katy: If a regular hexagon is inscribed in a circle of radius 6.72 centimeters, find the length of one side of the pentagon. How would I got about explaining this? Answered by Penny Nom. 





The length of each side of a regular ngon 
20061206 

From Shannen: The problem is: Find the length of each side of a regular ngon when a=80ft, n=20ft, and A is approx. 20,000 square feet. What do "a" and "n" stand for and how do I find the side length of an ngon? Answered by Penny Nom. 





The area of an irregular hexagon 
20061030 

From Ashish: I want to find out area of an irregular HEXAGON in square feet, whose sides are as follows, Answered by Stephen La Rocque. 





The area of a regular octagon 
20061022 

From Farhana: I have a regular octagon with sides of 0.8m and I need to find the area, Answered by Karen McIver and Penny Nom. 





Is a circle a regular shape? 
20061010 

From David: Is a circle a regular shape or an irregular shape? Answered by Stephen La Rocque. 





The area of an irregular octagon 
20060823 

From Billy: How do you figure the area of an irregular octagon? Measurements are 4 equal sides of =BD", and 4 equal sides of =BE". It measures 1 1/2" = from flat to flat. Answered by Penny Nom. 





The area of a lot 
20060805 

From Lyn: I have no idea how to find the square feet of an uneven polygon. I am in the process of making a land agreement and need to know.
Please tell me how to figure out the footage and acreage of land as follows.
roadfront 360'
back 360'
left side 220'
right side 180' Answered by Penny Nom. 





An irregular quadrilateral 
20060204 

From Christopher: Is there such a shape as an irregular quadrilateral with 4 equal sides? Answered by Penny Nom. 





Subdividing a polygon into triangles 
20060126 

From Adam: is there an algorithm to divide a regular polygon into N
equilateral triangles having the same area (no limit on N), or if not, an
algorithm to divide a regular polygon into N triangles having the same shape
and size? Answered by Chris Fisher. 





An irregular octagon 
20060120 

From Robert: I am building a poker table which is in the shape of an irregular octagon. I know the table measures 72 inches long and 48 inches wide with two parallel straight sides of equal length and six smaller sides of equal length ( three at each end of the table), what I don't know are the lengths of the any of the sides. Answered by Harley Weston. 





The area of an irregular semicircle 
20051014 

From Bob: Is there a way to compute the area of an irregular semicircle i.e. one in which the arc length is not determined by the diameter; and is therefore not technically any part circular  yet still possessing an arched side? Answered by Penny Nom. 





The area of a lot 
20040109 

From Lea:
I have a problem. I am interested in purchasing a piece of property which has the following dimensions. It is 259.10 Feet on the north side x 61.20 Feet on the east side x 217.80 Feet on the south side x 196.70 Feet on the west side. It looks like an irregular rectangle shape. How do you figure out the square footage on this irregular sized property, and what is the correct square footage answer.
I have attached a survey map. Answered by Harley Weston. 





The angles in a regular polygon 
20031221 

From Ernie: If i have a measure of one interior angle of a polygon, how can i find the number of sides it has? Answered by Penny Nom. 





The volume of an irregular tetrahedron 
20031124 

From Peter: How do I calculate the volume of an irregular shaped tetrahedron where: side a = 1.4 m side b = 1.4 m side c = 1.2 m and height = 0.75 m at the junction of sides a and b. Answered by Penny Nom. 





A circle around an irregular polygon 
20031103 

From Dale: How do I find the properties of a circle that is drawn around an irregular polygon of (n) sides with the lenghts of each side given and all end points of the polygon lye on the circumferance of the circle? Answered by Chris Fisher. 





The area of an odd shaped piece of property 
20030724 

From Barry: What is the formula for figuring the square footage of an odd shaped piece of property? Answered by Penny Nom. 





A regular polygon 
20030226 

From Melissa: The measure of each interior angle of a regular polygon is eight times that of an exterior angle of the polygon. How many sides does the polygon have? Answered by Penny Nom. 





The area of a regular ngon 
20030122 

From Sophie:
We have been given a piece of maths coursework. A farmer has exactly 1000 metres of fencing and wants to fence off a plot of level land. she does not mind what the shape is but it must have a perimeter of 1000m. She wants to fence off the plot of land which contains the maximum area. Investigate the shape, or shapes that could be used to fence in the maximum area using exactly 1000 metres of fencing each time. I have investigated many shapes, and I feel that a circle will have the biggest area. However we have also been asked to investigate shapes with 20 and 30 sides. My dad said that there is a formula for finding out any area of land. Do you know of this formula, if so I would be very grateful if you were to email it to me. Answered by Penny Nom. 





An octagon of perimeter 1,000 meters 
20021105 

From Stephen: my son has to work out the area of a octagon with a outside perimeter of 1,000 metres, Answered by Penny Nom. 





Regular polyhedra 
20020607 

From Sandra: The other day a colleague and I were talking about polyhedra. Is regular a term applied to polyhedra or just polygons? If so, then what would define a regular polyhedron? Would it mean all faces are regular or would it mean that all faces are identical and regular? That is, could a pyramid with equilateral triangles for lateral faces and a square base be considered regular or must the base also be an equilateral triangle? Answered by Chris Fisher. 





If you conect all the vertices of a regular ngon... 
20020401 

From Murray: If you conect all the vertices of a regular ngon with lines you will have (n3)(n/2) lines inside the polygon. I want to find out how many sections these lines divide the polygon into and how many intersections they have with each other. Answered by Claude Tardif. 





Area of a regular polygon 
20010501 

From Carl: What is the formula for finding the area of a regular Hexagon and a regular Pentagon Answered by Penny Nom. 





The area of platts 
20010220 

From Steve: I have to calculate the areas of different "platts" of land from a map, and the only thing I have are the four side measures. There are some cases where no sides are parallel, no lengths the same, and no angles are given, and I was wondering how to calculate the area of such figures. I've attached a rough sketch of a typical platt's shape. Answered by Walter Whiteley. 





An irregular polygon 
20010209 

From Jason: I have a 5 sided irregular polygon I am trying to figure out the area of. There are no right angles in the polygon as far as I can tell. I do not know any angles. Answered by Chris Fisher. 





Regular and irregular shapes 
19991003 

From Samuel Tighe: What is the difference between a regular shape and an irregular shape? Are a rectangle and a triangle regular or irregular shapes? Answered by Walter Whiteley. 





Area of an irregular shaped objects. 
19990407 

From Jesse Townsend: How do I find the surface area of an irregulary shaped object such as someone's knee from the thigh to shin? Thanks. Answered by Walter Whiteley. 





Angles in Polygons 
19990121 

From Jen:
 How do u find the interior angles of a pentagon when you are given 4 of the angles and you need to find the fifth?
 If you are given the measure of each exterior angle of a regular polygon, how do you figure out how many sides the polygon has?
 i need all information on polygons and how to find their angles!!!
Answered by Jack LeSage. 





A Hexagon 
19980922 

From Lee Curtis: Could someone calculate this for me? If a hexagon is 38 feet 8 inches across, how wide would each of the six sides be? Thank you, Lee Curtis Answered by Chris Fisher and Harley Weston. 





Sides in a Regular Polygon 
19961206 

From Rick Moss: If you are given the measure of each interior angle (162 degrees) of a regular polygon. How many sides does the polygon have? Answered by Penny Nom. 

