Before getting to the question on «how to find the area of a trapezoid », first let’s figure out what a trapezoid and an area of a trapezoid are. Trapezoid is a figure with four sides, so it is a quadrilateral, because quadrilaterals are figures with four sides. However, two sides of a trapezoid are parallel and the other two sides are not. Its parallel sides are called the base of a trapezoid, and the other two are called the legs or the lateral sides. So, a trapezoid is a quadrilateral figure with one pair of parallel sides. The distance between the two bases of a trapezoid is height.
The expression «trapezoid» has been in application in the English language since 1570, from Greek «trapezion» and from Late Latin trapezium, which word for word means a «small table». On the book «Elements» by Euclid, Marinus Proclus at first described «trapezion» when writing the commentary.
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There are some disputes about whether parallelograms with two pairs of parallel sides should be considered as trapezoids. Some people define a trapezoid as a quadrilateral with just one couple of parallel sides (the exclusive determination), which excludes parallelograms. Others, however, define a trapezoid as a quadrilateral with at least one pair of sides that are parallel (the inclusive determination), making quadrilaterals a special kind of trapezoid. The latter determination is consistent with its applications in higher mathematics. The former definition would make concepts like trapezoidal approximation to a definite integral ill-defined.
According to the inclusive determination, all parallelograms (rectangles, rhombuses, and squares) are trapezoids. Rectangles have reflex symmetry on mid-edges. Rhombuses have reflex symmetry on vertices. Squares have reflex symmetry on both vertices and mid-verges.
A Saccheri quadrilateral is very alike to a trapezoid in the hyperbolic plane with two adjoining right angles, however in the Euclidean plane it is a rectangle. In the hyperbolic plane a Lambert quadrilateral has three right angles.
A tangential trapezoid is a trapezoid with an incircle.
If quadrilateral is convex, the following properties are reciprocal, and each assumes that the quadrilateral is a trapezoid:
If when writing a reflective essay, you need to measure a trapezoid’s area, here is the easy explanation on how to do it:
All these actions form the formula that measures the trapezoid’s area, which is the following: [(a + b) x h]/2. Now you know how to find the area of a trapezoid using the main formula.
In 499 AD, a great mathematician-astronomer from the classical time of Indian mathematics and astronomy used this formula in the Aryabhata. This yields as a special case the well-known formula for the triangle area by considering a triangle as a degenerate trapezoid, where one of the parallel sides has shrunk to a point.
Let’s remember what the median is, before getting to the point on «how to find the area of a trapezoid». It is a line that connects the points of the sides that are non-parallel. The length of the median is the average of the two parallel sides. If you have a given value of a meridian then you can measure the trapezoid area following this formula: Area = mh, where m is the median and h is the height.
One more way that helps you to find out how to find the area of a trapezoid is to treat it as some plainer shapes, and then subtract or add their areas to find the result. For example, a trapezoid could be treated to a rectangle of a smaller shape with two right triangles. There are many ways for calculating the area of a triangle. Exactly how you do it depends on what values you are given at the start. As this can be very diverse, there is no an easy way to do it.
When doing a research summary in coordinate geometry, if the coordinates of the four vertices are given, you can calculate different properties of it, including the perimeter and the area.
In order to find a base of a trapezoid, give the one of the bases, the area, and the height. The main formula that gives an answer on how to find the area of a trapezoid has four variables (two bases, area, and the height). If you know those three variables you can easily calculate the fourth one. So, for example, if you know the height, the area, and one base, you can find the other base. In order to find that, follow this formula: Base length = (2a/h)-b, where a is the area, b is the known base, and h is the height.
The main formula that explains how to find the area of a trapezoid has four variables (two bases, the area, and the height). If you know those three variables, you can easily measure the fourth one. For example, if you know the two bases and the area, you can find the height, by easily reposition the main formula: Height = (2a)/(b1+b2), where a is the area, and b1, b2 are the bases.
All the trapezoids can be divided into two triangles. In this case, if you find the area of each two triangles and then add it up together, you will get an area of a trapezoid. In order to find the area of a triangle, you need to use this formula: A = (bxh)/2. Let’s say that the base of the bottom triangle is 6 cm and its height is 5 cm. So, that gives us A = (6x5)/2 = 15 cm2. Now, you can find the area of the top triangle. For example, its base equals 4 cm, and its height is the length of the line segment drawn from its upper vertex down to its base, so this height is exactly the same as of the other bottom triangle. So, the A = (bxh)/2 and this gives us A = (4x5)/2 = 10 cm2. Now, we know that the area of one triangle is 15 cm2 and the area of the other triangle is 10 cm2. And now, you can add the areas together to get the area of a trapezoid: A = 15 cm2 + 10 cm2 = 25 cm2. This value is the same as the one we got when used the main formula for calculating a trapezoid’s area. Now, you know where the main formula comes from and how to find the area of a trapezoid in different ways.
When writing an essay introduction you can specify more details on the term trapezium. In the U.S., for example, a trapezium is sometimes determined as a quadrilateral without parallel sides with the shape that is usually called an irregular quadrilateral. Once in Britain and elsewhere, the term trapezoid was defined as a quadrilateral without any parallel sides.
Oxford English Dictionary states that the sense of a figure that has no parallel sides is the meaning for which Proclus introduced the term trapezoid. This is kept in the French trapézoïde, German trapezoid, and other languages, although it is not used anymore. In Proclus’s sense a trapezium is a quadrilateral, which has one pair of its opposite sides parallel. This sense was specific in England in 17th and 18th centuries, and the prevalent one in recent use. A trapezium described as any quadrilateral is more general than a parallelogram is the sense of Euclid’s term. The sense of a trapezium as an irregular quadrilateral with no parallel sides was once used in England from 1800 to 1875.
In geometry, a trapezoid is used in the crossed ladder puzzle – the problem of finding the distance between the two parallel sides of a right trapezoid, when the values of the diagonal length and the distance from the perpendicular leg to the diagonal intersection are given.
In architecture the word is applied to describe symmetrical doors, windows, and buildings built wider at the base, getting refined to the top (mostly in Egyptian style). If the buildings have even sides and sharp anguled corners, their shapes are usually referred to as isosceles trapezoids. This shape was a standard style of doors and windows of the Incas.
In taxonomy, morphology, and other descriptive disciplines, where the term to describe shapes is necessary, trapezoid commonly is applied in descriptions of certain forms or organs.
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