In a rectangular trapezoid, the sides are 5 and 19 cm, and the larger base is 20 cm. Find the area of the trapezoid
February 18, 2021 | education
| 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.
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