In a trapezoid ABCD with base AD and BC, AD = 12; BC = 8 and the area is 100. Find the height of the trapezoid.

A trapezoid is a quadrilateral in which only two sides are parallel and the sides are not equal.

The area of the trapezoid is equal to the product of its midline by the height:

S = m h, where:

S is the area of the trapezoid;

m – middle line;

h – height.

In order to calculate the height of the trapezoid, you need to divide its area by the length of the midline:

h = S / m.

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

m = (a + b) / 2;

m = (8 + 12) / 2 = 20/2 = 10 cm.

h = 100/10 = 10 cm.

Answer: The height of the trapezoid is 10 cm.