Question

ABCD is a trapezium. AB || CD and E is the mid point of side BC . Prove that ar(AED) = 1/2 ar(ABCD).
Answer fast pls.....

Answer 1

ABCD is a trapezium such that AB || DC.

E is the mid-point of BC.

To prove: area(∆ABE)+area(∆DEC)=1/2 x area(trapezium ABCD)

proof:
area(∆ABE) = 1/2xarea(∆ABC) ..........(1) [since the median divides the triangle into equal parts]

similarly area(∆DEC) = 1/2xarea(∆BDC)...........(2)

area(∆BDC)=area(∆ADC) [triangles formed between same pair of parallel lines and with the same base are equal in areas]

∴ area(∆DEC)=1/2xarea(∆ADC)...........(3)

adding equ(1) and equ(3)

area(∆ABE)+area(∆DEC) = 1/2x[area(∆ABC)+area(∆ADC)] =1/2xarea(trapezium ABCD)