Area of parallelogram

Question

Trapezium ABCD and ADEF have the same height and the ratio of their areas is 13:14. If AD =10 cm and BC = 16 cm , find the length of EF.

Answer 1

Let x = length of EF and let h = height of each trapezoid 

 

Area of ABCD = (1/2)h(10+16)

 

Area of ADEF = (1/2)h(10+x) 

 

Then 13/14 = [(1/2)h(26)]/[(1/2)h(10+x)]

 

        13/14 = 26/(10+x)

 

        13(10+x) = 364

 

            10+x = 28

 

                 x = 18