# In the trapezoid ABCD with a right angle at the apex C, the base BC = 15cm and the sides

In the trapezoid ABCD with a right angle at the apex C, the base BC = 15cm and the sides AB = 17cm, CD = 8cm are known. Find the area of the trapezoid.

The area of the trapezoid is equal to the product of the half-sum of its bases and the height.

In this case, the known height is equal to the side CD = 8 cm and one base BC = 15 cm.

If BC is a larger base, you need to calculate how much larger it is. To do this, the height AK is lowered from the vertex A and the triangle AKB is considered, in which the leg AK = 8 cm, the hypotenuse AB = 17 cm.The second hypotenuse, according to the Pythagorean theorem, is 15 cm.

This means that the proposed figure is a right-angled triangle with an area of 0.5 * 15 * 8 = 60 cm ^ 2.

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