ABCD is a quadrilateral in which AB ∥ DC, and E and F are the midpoints of the diagonals AC and BD, respectively.
If AB = 30 cm, BC = 20 cm, DC = 86 cm and AD = 84 cm, then what is the length (in cm) of EF?​

Correct option is A

Given:

ABCD is a quadrilateral where AB ∥ DC.

E and F are midpoints of diagonals AC and BD respectively.

AB = 30 cm, BC = 20 cm, DC = 86 cm, AD = 84 cm.

Concept Used:

In a trapezium (AB ∥ DC), the line segment joining the midpoints of diagonals (EF) is equal to half the difference of the lengths of the parallel sides.

Formula Used:

EF = $$\frac{1}{2} \times |DC - AB|$$​​

Solution: 

EF = $$\frac{1}{2} \times |86 - 30| = \frac{1}{2} \times 56 = 28 \text{ cm}$$​​