The height drawn from the apex of the obtuse angle of the rectangular trapezoid will cut off the square

The height drawn from the apex of the obtuse angle of the rectangular trapezoid will cut off the square, the area of which = 16cm. Find S of a trapezoid if its obtuse angle = 135 (degrees).

Since, by condition, the quadrangle ABCN is a square, and its area is 16 cm2, the side of the square will be equal to: AB = BC = CD = AH = √Skv = √16 = 4 cm.

In a right-angled triangle СDН, we define the values of acute angles. Angle DСН = ВСD – ВСН = 135 – 90 = 45, angle СDН = 180 – СНD – DCН = 180 – 90 – 45 = 45.

The triangle CDH is isosceles and rectangular, AH = DH = 4 cm.

Then the base AD = AH + DH = 4 + 4 = 8 cm.

Determine the area of the trapezoid.

S = (AD + BC) * CH / 2 = (8 + 4) * 4/2 = 24 cm2.

Answer: The area of the trapezoid is 24 cm2.