In an isosceles trapezoid, the height drawn from an obtuse one divides the larger base into two parts

| March 2, 2021 | education

In an isosceles trapezoid, the height drawn from an obtuse one divides the larger base into two parts, the larger part is 20 cm, find the area of the trapezoid if its height is 12 cm.

First way.

Let’s draw the diagonals ВD and АС of the trapezoid, and through the point С we draw a straight line SK parallel to ВD.

ВСКD – parallelogram, then DК = ВС.

The segment AK = AD + DA = AD + BC, that is, it is equal to the sum of the lengths of the bases of the trapezoid. Since the CH height is the same for both the triangle and the trapezoid, their areas are equal.

In an isosceles trapezoid, the lengths of the diagonals are equal, then the ACK triangle is isosceles, and the height of CH is the median of the triangle, then AK = 2 * AH = 2 * 20 = 40 cm.

Define Sask = Savsd = AK * CH / 2 = (BC + AD) * CH / 2 = 40 * 12/2 = 240 cm2.

Second way.

The height of the trapezoid, drawn from the top of an obtuse angle, divides the larger base into two segments, the larger of which is equal to the half-sum of the bases, that is, the middle line of the trapezoid.

Then Savsd = AD * CH = 20 * 12 = 240 cm2.

Answer: The area of ​​the trapezoid is 240 cm2.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.