Find the length of the middle isosceles trapezoid if its lateral side, height and larger base, respectively, are 5; 4 and 9.

univerkov | June 21, 2021 | education

1. Vertices of the trapezoid – A, B, C, D. AB = BC = CD. BK height – 4 units. AB = 5 units of measure. AD = 9 units. MН is the middle line.

2. AK = √AB² – BK² = √5² – 4² √25 – 16 = √9 = 3 units.

3. The ABCD trapezoid is isosceles, therefore, according to its properties, the AK segment is calculated by the formula:

AK = (AD – BC) / 2 = 3 units.

АD – ВС = 6 units of measurement.

ВС = АD – 6 = 9 – 6 = 3 units.

МN = (АD + ВС) / 2 = (9 + 3) / 2 = 6 units of measurement.

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