The diagonal of an isosceles trapezoid is 10 cm, the middle line is 6 cm. Determine the distance between

| September 26, 2021 | education

The diagonal of an isosceles trapezoid is 10 cm, the middle line is 6 cm. Determine the distance between the bases of the trapezoid.

1. Vertices of the trapezoid A, B, C, D. AC – diagonal. MK is the middle line.

2. From the top of C we draw the perpendicular CH to the base of AD (it is the distance between the bases that needs to be calculated).

3. The length of the center line is calculated by the formula:

MK = (BC + AD) / 2.

4. The same formula is used to calculate the length of AH – the largest of the segments into which the height of CH is divided by the base AD.

Therefore, AH = MK = 6 cm.

5. We calculate the length of the height CH (the distance between the bases of the trapezoid). For the calculation, we use the Pythagorean theorem:

CH = √AC² – AH² = √10² – 6² = √100 – 36 = √64 = 8 cm.

Answer: the distance between the bases of the trapezoid is 8 cm.



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