Find the smaller side of the rectangle of the trapezoid, the base of which are equal to 10s and 6cm.

Find the smaller side of the rectangle of the trapezoid, the base of which are equal to 10s and 6cm. And one of the angles is 45 degrees.

Given:

rectangular trapezoid ABCE,

ВС and АЕ – bases,

BC = 6 centimeters,

AE = 10 centimeters,

angle E = 45 degrees.

Find the length less than the side of the trapezoid rectangle, that is, AB -?

Decision:

Consider a rectangular trapezoid ABCE. Let’s draw the height of the CH. We get the rectangle ABCH. He has AB = CH and AH = BC = 6 centimeters. So HE = AE – AH = 10 – 6 = 4 (centimeters).

Consider a right-angled triangle CHE. Angle C = 180 – 90 – 45 = 45 (degrees). Therefore, the CHE triangle is isosceles. Then CH = HE = AB = 4 centimeters.

Answer: 4 centimeters.