In an isosceles trapezoid ABCD, a perpendicular drawn from vertex B to the larger base AD of the trapezoid divides

| January 7, 2021 | education

In an isosceles trapezoid ABCD, a perpendicular drawn from vertex B to the larger base AD of the trapezoid divides it into segments equal to 4 cm and 10 cm. Find the bases and the midline of the trapezoid.

The height of the ВK, by condition, divides the larger base into segments AK = 4 cm, and KD = 10 cm.
Let us lower the height CM from point C to the base of the blood pressure. Since the trapezoid is equilateral, the CM height will also cut off the segment MD = AK = 4 cm.
Determine the length of the smaller base of the trapezoid.
BC = AD – AK – MD = 14 – 4 – 4 = 6 cm.
Let’s draw the middle line OH of the trapezoid, which is equal to half the sum of the lengths of the bases of the trapezoid.
OH = (BP + BC) / 2 = (14 + 6) / 2 = 10 cm.
Answer: AD = 14 cm, BC = 6 cm, OH = 10 cm.



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