# AB || DC of a trapezium ABCD and E is midpoint of BC. Let’s prove that area of triangular region AED = × area of trapezium shaped region ABCD.

Given.

AB || DC of a trapezium ABCD and E is midpoint of BC

Formula used.

Median of triangle divides it into 2 equal parts As E is midpoint of BC

In triangle ABC

AE is median

Triangle ABE = × triangle ABC

2 × triangle ABE = triangle ABC ……eq 1

In triangle BDC

DE is median

Triangle DEC = × triangle DBC

2 × triangle DEC = triangle DBC ……eq 2

In triangle ADC and triangle DBC

Both are on same base DC

And AB || CD

Putting value from eq 2

Triangle ADC = 2 × triangle DEC ……eq 3

We get ;

triangle ADC + triangle ABC = 2 × [Δ ABE + triangle DEC]

Trapezium ABCD = 2 × [trapezium ABCD – triangle AED]

2 × triangle AED =trapezium ABCD

Area of triangle AED = × trapezium ABCD

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos  Master Theorems in Circles42 mins  Quiz | Area and Parallelogram46 mins  Champ Quiz | Area of Triangle53 mins  Quiz | Surface Area & Volumes49 mins  NCERT | Imp. Qs. on Area of Parallelogram and Triangles43 mins  Proof of Important Theorems of Circles45 mins  Champ Quiz | Area of Parallelogram55 mins  NCERT | Imp Qs on Area of Parallelogram And Triangles44 mins  Surface Area of Right Circular Cylinder52 mins  Quiz | Mensuration42 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 