# The large diagonal of a rectangular trapezoid is 15 cm, and the larger base

October 3, 2021 | education

| **The large diagonal of a rectangular trapezoid is 15 cm, and the larger base is 12 cm.Find the area of the trapezoid if its smaller base is exactly 6 cm**

Since trapezoid ABCD is rectangular, its lateral side AB is also the height of the trapezoid.

From the right-angled triangle ABD, we determine, by the Pythagorean theorem, the height AB.

AB ^ 2 = BD ^ 2 – AD ^ 2 = 15 ^ 2 – 12 ^ 2 = 225 – 144 = 81.

AB = 9 cm.

Determine the area of the trapezoid.

Savsd = (BC + AD) * AB / 2 = (6 + 12) * 9/2 = 81 cm2.

Answer: The area of the trapezoid is 81 cm2.

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