The sides AB and CD of trapezoid ABCD are 36 and 39, respectively, and the base BC is 12.

| February 12, 2021 | education

The sides AB and CD of trapezoid ABCD are 36 and 39, respectively, and the base BC is 12. The bisector of angle ADC passes through the midpoint of side AB. Find the area of the trapezoid.

Let’s perform additional constructions. From the middle of the AB side, draw a line until it intersects with the opposite side so that it is parallel to the bases, that is, a middle line is formed. Let us prove that it is equal to half of the side of CD. This will find the length of the AD base. To find the height, draw a segment: from point B, draw a line BM to the intersection with the base so that it is parallel to CD and determine the area of ​​triangle ABM. Using Heron’s formula, we find the area and height of the triangle and at the same time the height of the trapezoid. Knowing the height and length of the bases, we determine the area of ​​the trapezoid.
Answer: 702



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