Shopping on line can be easy, simple and save you lots of money. It can also take a lot of your time, frustrate you, and result in unwanted purchases. Now the same can be said for regular high street shopping, but with the vast opportunity presented by the Internet it will pay you to spend a few minutes reading this and understanding how to better optimize your Trapezoid shopping experience:
1. Compare - without doubt the biggest advantage that the Trapezoid offers shoppers today is the ability to compare thousands of Trapezoid at a time. This is a great thing, but not necessarily all the time! Too much can be daunting at times so take advantage of the great comparison sites and where possible let them do the hard work for you.
2. Research - if it has been said it will be on the internet. Ignorance is no longer a justifiable reason for buying the wrong thing. Take the time to research in detail everything that you could possible want to know about
3. Testimonials - don't know anybody that has bought a Trapezoid? Wrong! If the Trapezoid is good the internet will let you know. Use the Internet as a friend and get testimonials before you buy.
4. Questions - Got a question about Trapezoid then search the Forums, FAQ's, Blogs etc. Don't be afraid to ask .....
5. Reputation - Never heard of the company selling Trapezoid? Don't worry, no reason why you should know every company in the world, but you know someone that does! Use the internet to find out what people are saying about Trapezoid and build up a picture of their reputation for sales, returns, customer service, delivery etc.
6. Returns - still worried that even after all of the above your Trapezoid wont be what you want? Check out the returns policy. There is so much competition now that someone, somewhere is bound to offer the terms that you are comfortable with.
7. Feedback - happy with your Trapezoid then let people know, after all you are depending on others people input in your buying decision, so why not give a little back.
8. Security - check for the yellow padlock on the Trapezoid site before you buy, and the s after http:/ /i.e. https:// = a secure site
9. Contact - got a question about Trapezoid, or want to leave a comment then check out the sites contact page. Reputable companies have them and respond.
10. Payment - ready to pay for your Trapezoid, then use your credit card or PayPal! Be aware of companies that don't accept them, there may be genuine reasons but given the huge amount of choice you have when buying online there is no reason at all not to buy via credit card or PayPal.
A
trapezoid (in North America) or
trapezium (in Britain and elsewhere) is a
quadrilateral, which is defined as a shape with
four sides, which has one set of parallel (geometry) sides. Some authors define it as a quadrilateral having
exactly one set of parallel sides, so as to exclude parallelograms.
The exactly opposite kind of quadrilateral, that is, one which does not have any parallel sides, is called a trapezium in North America and a trapezoid in Britain and elsewhere. This article uses the North American wording. It also admits parallelograms as special cases of trapezoids (however, in this case, it is assumed that one set of parallel sides is distinguished, and is the one referred to as "the set of parallel sides").
In an isosceles trapezoid, the base angles are congruent, and so are the pair of non-parallel opposite sides.
If the other set of opposite sides is
also parallel, then the trapezoid is also a
parallelogram. Otherwise, the other two opposite sides may be extended until they meet at a point, forming a triangle (geometry) that the trapezoid lies inside.
A quadrilateral is a trapezoid
if and only if it contains two adjacent
angles that are
supplementary angles, that is, they add up to one straight angle of 180 degree (angle)s (
pi radians). Another necessary and sufficient condition is that the
diagonals cut each other in mutually the same
ratio; this ratio is the same as that between the lengths of the parallel sides.
The midsegment (occasionally referred to as the median) of a trapezoid is the segment that joins the midpoints of the other set of opposite sides. It is parallel to the two parallel sides, and its length is the
arithmetic mean of the lengths of those sides.
The
area of a trapezoid can be computed as the length of the midsegment, multiplied by the distance along a
perpendicular line between the parallel sides. This yields as a special case the well-known formula for the area of a triangle, by considering a triangle as a degenerate trapezoid in which one of the parallel sides has shrunk to a point.
Thus, if
a and
b are the two parallel sides and
h is the distance (height) between the parallels, the area formula is as follows:
A= \frac{(a+b)h}{2}.
The quantity \frac{a + b}{2} is the
average of the horizontal lengths of the trapezoid, so the area can be understood to be the product of the average length and height of the shape.
Another formula for the area can be used when all that is known are the lengths of the four sides. If the sides are
a,
b,
c and
d, and
a and
c are parallel (where
a is the longer parallel side), then:
A=\frac{a+c}{4(a-c)}\sqrt{(a+b-c+d)(a-b-c+d)(a+b-c-d)(-a+b+c+d)}.
This formula does not work when the parallel sides
a and
c are equal since we would have division by zero. In this case the trapezoid is necessarily a parallelogram (and so
b =
d) and the numerator of the formula would also equal zero. In fact, the sides of a parallelogram aren't enough to determine its shape or area, the area of a parallelogram with sides
a and
b can be any number from "
a b" to "zero".
When the smaller parallel side
c is set to zero, this formula turns to be Heron's formula.
If the trapezoid above is divided into 4 triangles by its diagonals
AC and
BD, intersecting at
O, then the area of Δ
AOD is equal to that of Δ
BOC, and the product of the areas of Δ
AOD and Δ
BOC is equal to that of Δ
AOB and Δ
COD. The ratio of the areas of each pair of adjacent triangles is the same as that between the lengths of the parallel sides.
External links
- "Trapezoid" on MathWorld
- Trapezoid definition Area of a trapezoid Median of a trapezoid With interactive animations
- Trapezoid (North America) at elsy.at: Animated course (construction, circumference, area)
A
trapezoid (in North America) or
trapezium (in Britain and elsewhere) is a
quadrilateral, which is defined as a shape with
four sides, which has one set of
parallel (geometry) sides. Some authors define it as a quadrilateral having
exactly one set of parallel sides, so as to exclude parallelograms.
The exactly opposite kind of quadrilateral, that is, one which does not have any parallel sides, is called a trapezium in North America and a trapezoid in Britain and elsewhere. This article uses the North American wording. It also admits parallelograms as special cases of trapezoids (however, in this case, it is assumed that one set of parallel sides is distinguished, and is the one referred to as "the set of parallel sides").
In an
isosceles trapezoid, the base angles are congruent, and so are the pair of non-parallel opposite sides.
If the other set of opposite sides is
also parallel, then the trapezoid is also a parallelogram. Otherwise, the other two opposite sides may be extended until they meet at a point, forming a triangle (geometry) that the trapezoid lies inside.
A quadrilateral is a trapezoid if and only if it contains two adjacent angles that are supplementary angles, that is, they add up to one straight angle of 180 degree (angle)s (pi
radians). Another necessary and sufficient condition is that the
diagonals cut each other in mutually the same ratio; this ratio is the same as that between the lengths of the parallel sides.
The midsegment (occasionally referred to as the median) of a trapezoid is the segment that joins the midpoints of the other set of opposite sides. It is parallel to the two parallel sides, and its length is the
arithmetic mean of the lengths of those sides.
The
area of a trapezoid can be computed as the length of the midsegment, multiplied by the distance along a perpendicular line between the parallel sides. This yields as a special case the well-known formula for the area of a triangle, by considering a triangle as a degenerate trapezoid in which one of the parallel sides has shrunk to a point.
Thus, if
a and
b are the two parallel sides and
h is the distance (height) between the parallels, the area formula is as follows:
A= \frac{(a+b)h}{2}.
The quantity \frac{a + b}{2} is the
average of the horizontal lengths of the trapezoid, so the area can be understood to be the product of the average length and height of the shape.
Another formula for the area can be used when all that is known are the lengths of the four sides. If the sides are
a,
b,
c and
d, and
a and
c are parallel (where
a is the longer parallel side), then:
A=\frac{a+c}{4(a-c)}\sqrt{(a+b-c+d)(a-b-c+d)(a+b-c-d)(-a+b+c+d)}.
This formula does not work when the parallel sides
a and
c are equal since we would have division by zero. In this case the trapezoid is necessarily a parallelogram (and so
b =
d) and the numerator of the formula would also equal zero. In fact, the sides of a parallelogram aren't enough to determine its shape or area, the area of a parallelogram with sides
a and
b can be any number from "
a b" to "zero".
When the smaller parallel side
c is set to zero, this formula turns to be Heron's formula.
If the trapezoid above is divided into 4 triangles by its diagonals
AC and
BD, intersecting at
O, then the area of Δ
AOD is equal to that of Δ
BOC, and the product of the areas of Δ
AOD and Δ
BOC is equal to that of Δ
AOB and Δ
COD. The ratio of the areas of each pair of adjacent triangles is the same as that between the lengths of the parallel sides.
External links
- "Trapezoid" on MathWorld
- Trapezoid definition Area of a trapezoid Median of a trapezoid With interactive animations
- Trapezoid (North America) at elsy.at: Animated course (construction, circumference, area)
Definition: trapezoid from Online Medical Dictionary
The Online Medical Dictionary is a searchable dictionary of definitions from medicine, science and technology.
Trapezoid - Wikipedia, the free encyclopedia
A trapezoid (in North America) or a trapezium (in Britain and elsewhere) is a quadrilateral (a closed plane shape with four linear sides) that has at least one pair of parallel ...
Isosceles trapezoid - Wikipedia, the free encyclopedia
An isosceles trapezoid (isosceles trapezium in British English) is a quadrilateral with a line of symmetry bisecting one pair of opposite sides, making it automatically a trapezoid ...
Trapezoid -- from Wolfram MathWorld
A trapezoid is a quadrilateral with two sides parallel. The trapezoid is equivalent to the British definition of trapezium (Bronshtein and Semendyayev 1977, p. 174). The trapezoid ...
Trapezoid Technologies
Trapezoid Website Solutions ... Need a Website Solution? Go with experience! Trapezoid is a pioneer in interactive communications and website development.
trapezoid - definition of trapezoid by the Free Online Dictionary ...
trap·e·zoid (tr p-zoid) n. 1. A quadrilateral having two parallel sides. 2. A small bone in the wrist, situated near the base of the index finger.
The Trapezoid
The trapezoid is a quadrilateral with one pair of parallel sides. The parallel sides of a trapezoid are called the bases, here symbolized by b 1 and b 2.
Order of the Trapezoid
Chivalric order of knighthood within the Temple of Set for adept black magicians who have sworn fealty beyond death.
Dictionary of Bridges
Trapezoid : A four-sided figure with one pair of parallel sides. Travertine : A pale form of limestone. Truss : A frame of members in tension and compression.
trapezoid - definition of trapezoid in the Medical dictionary - by the ...
trapezoid /trap·e·zoid/ (trap´e-zoid) 1. having the shape of a four-sided plane, with two sides parallel and two diverging. 2. the bone in the distal row of carpal bones lying ...
