Find the midline of an isosceles trapezoid with a base angle of 45 degrees if its smaller base is 8 cm

univerkov | May 23, 2021 | education

Find the midline of an isosceles trapezoid with a base angle of 45 degrees if its smaller base is 8 cm and its height is 5 cm.

1. The tops of the trapezoid – A, B, C, D. BC = 8 cm – a smaller base. BK = 5 cm (drawn to the base of AD). ∠А = 45 °. МN is the middle line.

2. We calculate the length of the segment AK through the tangent ∠А:

BK: AK = tangent ∠A = tangent 45 ° = 1.

AK = BK: 1 = 5: 1 = 5 cm.

3. In an isosceles trapezoid, the length of the segment AK is (AD – BC) / 2 (according to its properties).

AK = (AD – BC) / 2 = 5 cm.

АD – ВС = = 10 cm.

AD = BC + 10 = 8 + 10 = 18 cm.

4.MN = (BC + AD) / 2 = (18 + 8) / 2 = 13 cm.

Answer: МN = 13 cm.

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