MR-689 / 9.) problem

An isosceles trapezoid with a base of 8 cm and 2 cm is described around a circle. Calculate the area of the trapezoid.

Since, according to the task, there is a tangent circle inside the trapezoid, so this trapezoid is a tangent quadrilateral! Therefore, the following relation can be written:

a+b=c+c

8+2=2c

2c=10

c=102

c=5

c2=a-b22+h2

52=8-222+h2

52=32+h2

25=9+h2

h2=25-9

h2=16

h=16

h=4

h=2·r

r=h2=42

r=2

A=s·r

s=a+b+c+c2=8+2+5+52=202

s=10

A=s·r=10·2

A=20