Definition of Trapezoid.
A trapezoid is a four-sided closed 2D figure which has an area and its perimeter. Two sides of a trapezoid are parallel to each other and they are termed as the bases of the trapezoid. The non-parallel sides are known as the legs or lateral sides of a trapezoid. The shortest distance between two parallel sides is known as the altitude. Since the opposite sides are parallel to each other, calculating the area of a trapezoid is simple.
Properties of Trapezoid.
These are the properties of a trapezoid that make it stand out from other quadrilaterals:
▪️The bases (the top and bottom) are parallel to each other.
▪️Opposite sides of a trapezoid (isosceles) are of the same length.
▪️Angles next to each other sum up to 180°.
▪️The median is parallel to both the bases.
▪️Median’s length is the average of both the bases i.e. (a +b)/2.
▪️If both pairs of the opposite sides are parallel in a trapezoid, it is considered a parallelogram.
▪️If both pairs of the opposite sides are parallel, all sides are of equal length, and at right angles to each other, then a trapezoid can be considered as a square.
▪️ If both pairs of the opposite sides are parallel, its opposite sides are of equal length and at right angles to each other, then a trapezoid can be considered as a rectangle.
Types of Trapezoid.
There are three types of trapezoids, and those are given below:
1. Isosceles Trapezoid.
If the legs or non-parallel sides of the trapezoid are equal in length, then it is called an isosceles trapezoid. The angles of the parallel sides (base) in the isosceles trapezoid are equal to each other. An isosceles trapezoid has a line of symmetry and both the diagonals are equal in length.
In the below isosceles trapezoid XYZW, XY and WZ are called the bases of the trapezoid. WX and YZ are called the legs of the trapezoid since they are not parallel to each other.
2. Scalene Trapezoid.
When neither the sides nor the angles of the trapezoid are equal, then it is a scalene trapezoid. In the below scalene trapezoid, all four sides i.e. AB, BC, CD, and DA are of different lengths. The bases i.e. DC and AB are parallel to each other but are of different lengths.
3. Right Trapezoid.
A right trapezoid also called the right-angled trapezoid, has a pair of right angles. These kinds of trapezoids are used to estimate the areas under the curve. In the below right trapezoid or right-angled trapezoid, there are two right angles one at D and the other one at A. One pair of opposite sides i.e. DC and AB are parallel to each other.
Area of Trapezoid.
The area of the trapezoid is calculated by measuring the average of the parallel sides and multiplying it with its height.
The area of a trapezoid is calculated by the following formula:
Area =[(AB + CD)/2] × hWhere AB and CD are the parallel sides and h is the height.
Perimeter of Trapezoid.
The perimeter of a trapezoid is the sum of all its sides. If A, B, C, D are the four sides of a trapezoid, then the perimeter formula is:
Perimeter = AB + BC + CD + AD