In a rectangular trapezoid, the sides are 5 and 19 cm, and the larger base is 20 cm. Find the area of the trapezoid

Let’s draw the height of the CH trapezoid. Since the trapezoid is rectangular, and CH is height, then the quadrilateral ABCH is a rectangle, then CH = AB = 5 cm, BC = AН.

In a right-angled triangle, we will determine the length of the DН leg using the Pythagorean theorem.

DН ^ 2 = СD ^ 2 – CH ^ 2 = 19 ^ 2 – 5 ^ 2 = 361 – 25 = 336.

Dн = 4 * √21 cm.

Then the length of the segment AH = AD – DН = 20 – 4 * √21 = 1.7 cm.

BC = AH = 1.7 cm.

Determine the area of the trapezoid.

Savsd = (ВС + AD) * CH / 2 = (1.7 + 20) * 5/2 = 54.25 cm2.

Answer: The area of the trapezoid is 54.25 cm2.