Find the area of an isosceles trapezoid if its smaller base is 4, its height is 5, and an obtuse angle is 135 degrees.

Let’s build the height of the CH trapezoid ABCD.

Angle DСН = ВСD – ВСН = 135 – 90 = 45.

Then the right-angled triangle СDН is isosceles, DH = СН = 5 cm, since one of its acute angles is 45.

Let’s build the height BK. Rectangular triangles ABK and СDН are equal in hypotenuse and acute angle, then AK = DH = 5 cm. The quadrilateral BCНK is a rectangle, which means KН = BC = 4 cm.

AD = AK + KH + DH = 5 + 4 + 5 = 14 cm.

Then Savsd = (BC + AD) * CH / 2 = (4 + 14) * 5/2 = 45 cm2.

Answer: The area of the trapezoid is 45 cm2.