In a rectangle ABCD A B is 6 centimeters BC is 8 centimeters. T belongs to the side BC in the quadrilateral

In a rectangle ABCD A B is 6 centimeters BC is 8 centimeters. T belongs to the side BC in the quadrilateral ABCD is an inscribed circle Calculate the area of the quadrilateral whose vertices are points A D the center of the circle C is the midpoint of the side CD

Point K, by condition, is the middle of CD, CK = CD / 2 = 6/2 = 3 cm.

The radius of the inscribed circle is equal to half of the lateral side, then OH = R = CD / 2 = 6/2 = cm.

Then KO is parallel to AD, and the required quadrilateral is a rectilinear trapezoid with bases AD OK and a right angle ADK.

The area of the trapezoid is equal to: Saokd = (OK + AD) * KD / 2.

OK = AD – OM = 8 – 3 = 5 cm.

Then Saokd = (5 + 8) * 3/2 = 39/2 = 19.5 cm2.

Answer: The area of the quadrangle is 19.5 cm2.