Question

In the quadrilateral ABCD, if AB//CD, E is mid-point of side AD, and F is mid-point of BC. If AB = 20 cm and EF = 16 cm, the length of side DC is:

Options

• 18 cm

• 12 cm

• 24 cm

• 32 cm

Answer 1

12 cm

Explanation:

The line segment joining the midpoints of the non-parallel sides of a trapezium is equal to half the sum of its parallel sides, given by the formula EF = `1/2` (AB + DC). Substituting the given values, `16 = 1/2 (20 + DC)`, which yields 32 = 20 + DC, resulting in DC = 12 cm.