Trapezoid Formula – Perimeter & Area of a Trapezoid Rule Formula

Trapezoidal Rule Formula

A quadrilateral with two parallel sides is called the Trapezoid. It may also be named as the Trapezium in major parts of the world.  The two sides that are parallel in Trapezoid are known as bases and the non-parallel sides are known as the lateral sides. And the distance between two parallel is named as the altitude.

There was an interesting argument between schools where one professor claimed that trapezoid has only one set of parallel sides while other professor claimed that it may have more than one set of parallel sides. Based on the second definition, it is considered that the Trapezoid is a special case of the parallelogram. At the same time, the first statement does not consider a parallelogram to be a Trapezium.

Trapezoid Formula

There are a number of properties that help you in identifying any quadrilateral as Trapezoid. These are –

  • The diagonals and the base angles of a trapezoid would be equal.
  • When a median is drawn on a Trapezoid then it is parallel to the base and its height would be the average length of its bases.
  • The point where diagonals intersect is colinear to the mid-points of the opposite sides.

The Perimeter of a Trapezoid Formula

The concept of Trapezoid is frequently used in various physics computations and advanced mathematics calculations. Also, this is a part of the study during school days and competitive exams too. If you wanted to go into engineering then a depth understanding of the concept is necessary. Here, we will discuss how to calculate the perimeter of a Trapezoid.

To calculate the perimeter, you need to sum up all four sides. For example, if there is one Trapezoid whose side lengths are a, b, c, and d then formula for calculating perimeter will be given as –

\[\large P=a+b+c+d\]

Where,
a, b, c, d are the lengths of each side.

Area of a Trapezoid Formula

You must be curious to know how to calculate the area of a trapezoid formula. Well. This is easy to calculate by taking the average of two bases and multiply it with the altitude. In mathematics, the area of a Trapezoid formula is given as –

\[\large Area\;of\;a\;Trapezoid\; = \frac{1}{2} \times h \times (a + b)\]
Where:
h = height (Note – This is the perpendicular height, not the length of the legs.)
a = the short base
b = the long base

Centroid of a Trapezoid Formula

As we discussed earlier, a Trapezoid is a quadrilateral with two parallel sides. The centroid of a Trapezoid lies somewhere between the two bases. The centroid of a trapezoid formula in mathematics is given as –

\[\LARGE x = \frac{b+2a}{3(a+b)}h\]

Where,
h = height of trapezoid
a and b = P
arallel sides,

Isosceles Trapezoid Formula

A quadrilateral is a four-sided shape with only one pair of parallel sides and non-parallel sides are equal in length. There are two popular types of Trapezoid – one is isosceles and the another is right-angled Trapezoid. The perimeter and the area of an isosceles Trapezoid is given as –

\[\large Perimeter\;of\;Isosceles\;Trapeziod=a+b+2c\]

Where,
a, b and c are the sides of the trapezoid

The Area of isosceles trapezoid formula is

\[\large Area\;of\;Isosceles\;Trapeziod=h\left [\frac{a+b}{2}\right]\]

Where,
a and b are the parallel sides of trapezoid.


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