The lengths of the base of the trapezoid are 28 and 12. Find the distance between the midpoints

univerkov | June 21, 2021 | education

The lengths of the base of the trapezoid are 28 and 12. Find the distance between the midpoints of the diagonal of the trapezoid

We will construct the middle line KM of the trapezoid ABCD, which divides the diagonals AC and BC at points P and H in half. Then the segment PH is our required segment.

In triangle ABC, point K is the middle of AB, point P is the middle of AC, then the segment KP is the middle line of triangle ABC, then KP = BC / 2 = 12/2 = 6 cm.

Similarly, MH = BC / 2 = 12/2 = 6 cm.

The length of the middle line of the trapezoid is: KM = (BC + AD) / 2 = (12 + 28) / 2 = 20 cm.

Then the length of the segment PH = (KM – KP – MN) = (20 – 6 – 6) = 8 cm.

Answer: Between the middle of the diagonals 8 cm.

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