Area of Trapezium

 This post about the Area of ​​Trapezium is going to get information. Along with that we will also see Trapezium of Perimeter and some Trapezium Examples. Friends, this is a part of the quadrilateral. Which we call trapezium. In this post, all the problems related to trapezium will be clear to you, so friends, let us all come to know in detail. Before that we need to know this. Finally what is a quadrilateral and is trapezium its parts. So this is all we are going to learn in this post. Let's go into detail-

What is Trapezium 

" A shape surrounded by four arms with only two sides equal is called trapezium." Trapezium are four-sided quadrilaterals like squares, rectangles, parallelograms, etc. You have learnt that a square and rectangle have sides that are at right angles to one another, where-as a rhombus and a parallelogram have sides that are parallel but not at right angles to each other. Let us revise about Trapezium. 

ABCD is a trapezoid, in which only AD and BC are parallel sides, but AB and CD are not parallel. AB and CD are vertical arms. If A is drawn from AE or D to DF perpendicular BC, AE or DF will be its height.

Note : Sum of all angles of a quadrilaterals is equal to 360⁰.

Types of Trapezium

There are the following types of trapezium-

• Isosceles Trapezium 
• Right Trapezium
• Scalene Trapezium

Area of a Trapezium

Devendra has a plot near the main road. The shape of the plot is not the same planar shape as rectangle, triangle or circle. The plot has only one pair with parallel facing arms. Therefore it is trapezoid in shape. To find the area of ​​this plot, we break it into two parts - one in the rectangle and the other in the area of ​​the triangular shape.

 Let ABCD is a trapezium in which AB || CD

Area of Trapezium = 1/2  X  height  X Sum of parallel arms

Proof that formula 

We know that, Area of a trapezium ABCD

= Let AB = a, CD = b 

and CF = DF = h 

Area of Trapezium ABCD = Area of Triangle 🔺 AED +  Area of ㅁRectangle CDEF +  Area of Triangle 🔺 BFC

                                           = 1/2 AE x DE + EF x + 1/2 FB x CF 

                                           = 1/2 AE x h + EF x + 1/2 FB x h 

                                           = 1/2 [ (AE + EF + FB) + EF ] x h

                                           = 1/2 [ (AE + EF + FB) + CD ] x h ( :. EF = CD )

                                           = 1/2 (a+b)h (:.AE + EF + FB = a )

Area of Trapezium = 1/2 ( Sum of parallel arms ) x hight

Area of Trapezium Formula

Area of Trapezium =   h( a + b )/ 2

Where,

         “a” and “b”  =    bases 

                       “h” =    height.

Perimeter of Trapezium

Perimeter = AB + BC + CD + DA