The bases of the trapezoid are 2 and 12, the area is 63. Find the height 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 area of a trapezoid is the product of the half-sum of its bases by the height:

S = (a + b) / 2 h, where:

S is the area of the trapezoid;

a – smaller base of the BC;

b – larger AD base;

h is the height of the trapezoid BH.

To find the height of the BH, we express it in terms of x.

Let’s make the equation:

(a + b) / 2 ∙ h = S;

(2 + 12) / 2 ∙ x = 63;

14/2 ∙ x = 63;

7 ∙ x = 63;

x = 63/7 = 9;

h = 9 cm.

Answer: HВ height is 9 cm.