The middle line of the trapezoid is 13. The area is 65. Find the height of the trapezoid.

The area of the trapezoid is equal to the product of the half-sum of the bases and the height.

S = (a + b) / 2 ∙ h.

The midline 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. Accordingly, the area of the trapezoid is the product of the midline and the height:

S = m ∙ h, where:

S is the area of the trapezoid;

m is the middle line of the trapezoid;

h – height.

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

h = S / m;

h = 65/13 = 5 cm.

Answer: The height of the trapezoid is 5 cm.