The middle line of the trapezoid is 28, the larger base is 40. Find the smaller base of the trapezoid.

A trapezoid is a quadrilateral in which one pair of opposite sides is parallel, and the sides are not equal to each other.

The middle line of a trapezoid is a line segment connecting the midpoints of the sides of the trapezoid. It is parallel to the bases, and its length is equal to half the sum of the bases:

m = (a + b) / 2; where:

m is the middle line of the trapezium NK;

a – the smaller base of the BC trapezoid;

b – larger AD base.

Thus:

HK = (BC + AD) / 2;

(BC + AD) = 2 ∙ HK;

ВС = 2 ∙ НК – АD;

BC = 2 ∙ 28 – 40 = 56 – 40 = 16 cm.

Answer: The length of the smaller base of the trapezoid is 16 cm.