In a rectangular trapezoid, the sides are 15 and 9 cm, and the larger base is 20 cm. Find the area of the trapezoid.

1. A, B, C, D – the tops of the trapezoid. Larger base АD = 20 cm. AB = 9 cm. СD = 15 cm.

2. From the top С we draw the height СН.

3. The opposite sides of the rectangle ABCH formed in this case are equal:

AB = CH = 9 cm. BC = AН.

4. Calculate the length of the segment DH:

DН = √СD ^ 2 – СН ^ 2 = √15 ^ 2 – 9 ^ 2 = √225 – 81 = √144 = 12 cm.

5. АН = АD – DH = 20 – 12 = 8 cm. ВС = 8 cm.

6. Area of the trapezoid = (BC + AD) / 2 x CH = (8 + 20): 2 x 9 = 14 x 9 = 126 cm ^ 2.

Answer: the area of the AVSD trapezoid is 126 cm ^ 2.



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