Question

ABCD is a trapezium with parallel sides AB=a units and DC=b units. If E and F are the midpoints of non-parallel sides AD and BC respectively, then what is the ratio of area (ABFE) to the area (EFCD)?​

Answer 1

given: AB = a units,

CD = b units,

E is mid of AD and F is mid of BC

to find:  area(trap. ABFE) : area(trap. EFCD)

now, we first need to find EF,

EF = (AB + DC )/ 2 = (a + b)  / 2  

So let's consider x = height ,

area(trap. ABFE) : area(trap. EFCD)

1/2 {a + (a+b / 2)} × x : 1/2 {b + (a+b / 2)}  × x

cancelling 1/2 and x from both sides

(2a + a + b )/ 2 :  (2b + a + b )/ 2  

3a + b : 3b + a