Find the area of a trapezoid ABCD with bases AD and BC, if AB = CD = 5 cm, BC = 7 cm, AD = 13 cm

Since, by condition, AB = CD = 5 cm, the trapezoid ABCD is isosceles.

Let’s build the height BH of the trapezoid ABCD.

Since the trapezoid is isosceles, the height ВН divides the base into two segments, the length of the smaller of which is equal to the half-difference of the lengths of the bases of the trapezoid.

AH = (AD – BC) / 2 = (13 – 7) / 2 = 3 cm.

In a right-angled triangle ABH, according to the Pythagorean theorem, we determine the length of the leg BH.

BH ^ 2 = AB ^ 2 – AH ^ 2 = 25 – 9 = 16.

BH = 4 cm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * ВН / 2 = (7 + 13) * 4/2 = 40 cm2.

Answer: The area of the trapezoid is 40 cm2.