The bases of the trapezoid are 3 and 2, the diagonals are 4 and 3. Find the area of the trapezoid.

Let’s draw a segment CК parallel to the diagonal ВD, then the quadrangle of the ВСКD is a parallelogram, and therefore, DK = ВС = 2 cm, СK = ВD = 4 cm.

The base of the AK of the triangle ACK is equal to: AK = AD + DK = AD + BC = 3 + 2 = 5 cm.

The area of the trapezium ABCD is equal to: Savsd = (BC + AD) * CH / 2.

The area of the triangle AСK is equal to: Sask = AK * CH / 2 = (BC + AD) * CH / 2.

Thus, Sask = Savsd.

Let us determine the area of the triangle ACK by Heron’s theorem.

The AСK semi-perimeter is equal to: p = (3 + 4 + 5) / 2 = 6 cm.

Then Sask = √6 * (6 – 3) * (6 – 4) * (6 – 5) = √6 * 3 * 2 * 1 = √36 cm2.

Sask = Savsd = 6 cm2.

Answer: The area of the trapezoid is 6 cm2.