In the trapezoid, the bases are 4cm and 12cm, and the height is equal to half the sum of the lengths

In the trapezoid, the bases are 4cm and 12cm, and the height is equal to half the sum of the lengths of the bases. Find the area 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 half the sum of its bases by the height:

S = (BC + AD) / 2 * h.

Let’s find the height of this trapezoid. Since its length is equal to the half-sum of the bases BC and AD:

h = (BC + AD) / 2;

h = (4 + 12) / 2 = 16/2 = 8 cm.

Now let’s find the area of the trapezoid:

S = (4 + 12) / 2 * 8 = 16/2 * 8 = 8 8 = 64 cm2.

Answer: the area of the trapezoid is 64 cm2.