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A trapezoid is a quadrilateral that has four parallel sides. In some parts of the world it is known as trapezium. This happens to be a four sided figure or shape that would cover some area and have a perimeter. It happens to be a 2 d figure and not a 3d figure. The sides that are parallel to each other are termed as bases of the trapezoid. Coming to the non- parallel sides it is known as the lateral sides or legs. Any form of distance between both the parallel sides is referred to as the altitude. The **area of trapezoid** is a point to consider.

Till this point of time there is a disagreement about the definition of trapezoid. A school of Maths does consider it as having one and only pair of parallel sides. Others would argue that could be more than one pair of parallel sides in a trapezoid. If we take the second definition a parallelogram is a trapezoid based on the inputs available. Though some experts do not consider a parallelogram to be a trapezoid. One thing that emerges it is already a pair of quadrilateral.

**The types of trapezoids**

The classification of trapezoids takes place in three groups. They are as follows

- Right trapezoid- such a type of trapezoid would be having a pair of right angles
- Isosceles trapezoid- if there are non- parallel sides then the legs of a trapezoid would be equal in length. It is known as an isosceles trapezoid.
- Scalene trapezium- it is a type of trapezoid where neither the sides or the angles would be equal

**The shape of a trapezoid**

As already discussed a trapezoid is a four shaped figure where one of the sides would be parallel. It occurs to be a two dimensional figure as it would be similar to square, rectangle or parallelogram. Hence this shape would also have an area along with a perimeter just like other shapes do. Once you are aware about the formula for the perimeter and area the task may become an easy one.

**The perimeter and area of a trapezoid**

Coming to the area of a trapezoid, it may be calculated as an average of both bases and then you would multiply it with the altitude. The formula of calculating

Area = ½( a+b) h

The perimeter of a trapezoid would be a sum of all the four sides. If a trapezoid has sides a, b, c and d then the formula of the trapezoid would be

Perimeter= a+ b+c+ d

For example the four sides would be measuring 3m, 5m,7m and 9 m. Since we are aware that perimeter would be the sum of all the four sides , So the perimeter in this case would be 26 m.

**Properties of trapezoid**

Below are mentioned some of the **properties of a trapezoid**

- The diagonals and base angles of an isosceles trapezoid is equal
- If you are drawing a median on a trapezoid, it would be parallel to the bases as the length is going to be an average of the bases
- An intersection point of the diagonals would be collinear to the points which is the midpoint of both of them.
- If a trapezoid has three sides a, b and c, with the diagonals p and q then the equation would be

**p ^{2}+q^{2}= c^{2}+d^{2}+2ab**

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