An isosceles trapezoid is given, the base of which is 1 dm and 4.2 dm. Find the side of the trapezoid

| April 22, 2021 | education

An isosceles trapezoid is given, the base of which is 1 dm and 4.2 dm. Find the side of the trapezoid if the distance between its bases is 3 dm.

The distance between the bases of the trapezoid is its height BH = 3 dm.

In an isosceles trapezoid, the height drawn from the apex of an obtuse angle divides the larger base into two segments, the smaller of which is equal to the half difference of the base lengths.

AH = (AD – BC) / 2 = (4.2 – 1) / 2 = 3.2 / 2 = 1.6 dm.

From the right-angled triangle ABH, according to the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = BH ^ 2 + AH ^ 2 = 3 ^ 2 + 1.6 ^ 2 = 9 + 2.56 = 11.56.

AB = 3.4 cm.

Since the trapezoid is isosceles, then CD = AB = 3.4 cm.

Answer: The side of the trapezoid is 3.4 cm.



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