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

July 27, 2021 | education

| 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.

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