In an isosceles trapezoid, one base is 6 more than the other, and the lateral sides serve

In an isosceles trapezoid, one base is 6 more than the other, and the lateral sides serve as the diameter of touching circles, each of which has a length of 5 Find the area of the trapezoid.

The length of the segment OO1 is equal to the sum of the radii of the circles, OO1 = (R + R) = (2.5 + 2.5) = 5 cm.

Since the points O and O1 are the centers of the circles, they are the midpoints of the lateral sides of the trapezoid, which means that the segment OO1 is the middle line of the trapezoid.

By condition, (АD – ВС) = 6 cm.Since ВС = НК, then (АD – НК) = 6 cm.

AD – HK = AH + DK = 6 cm.

Since the trapezoid is isosceles, then AH = DK, then AH = DK = 6/2 = 3 cm.

In a right-angled triangle ABN, BH ^ 2 = AC ^ 2 – AH ^ 2 = 25 – 9 = 16 cm.

BH = 4 cm.

Find the area of the trapezoid. Savsd = OO1 * VN = 5 * 4 = 20 cm2.

Answer: The area of the trapezoid is 20 cm2.




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