A circle is inscribed in a rectangular trapezoid from the base of 6 and 7, find S area.
| July 1, 2021 | education
Let’s build the height of the CH trapezoid.
In a right-angled triangle СDН, the length of the segment is DH = AD – AH = AD – BC = 7 – 6 = 1 cm.
Then, by the Pythagorean theorem, CD ^ 2 = CH ^ 2 + DH ^ 2 = AB ^ 2 + 1. (1).
Since a circle is inscribed in the trapezoid, AB + CD = BC + AD = 13.
AB + CD = 13. (2).
Let’s solve the system of equations 1 and 2.
AB = 13 – CD.
CD ^ 2 = (13 – CD) ^ 2 + 1.
CD ^ 2 = 169 – 26 * CD + CD ^ 2 + 1.
26 * CD = 170.
CD = 170/26 = 85/13.
AB = 13 – 85/13 = 84/13 cm.
Determine the area of the trapezoid.
Savsd = (BC + AD) * AB / 2 = 13 * (84/13) / 2 = 42 cm2.
Answer: The area of the trapezoid is 42 cm2.
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