In an isosceles trapezoid, the obtuse angle is 135 degrees, and the height is 3 times

In an isosceles trapezoid, the obtuse angle is 135 degrees, and the height is 3 times less than the larger base. Find the area of the trapezoid if the smaller base is 6 cm.

Let the height of the trapezoid be X cm, then the base AD = 3 * X cm.

In a right-angled triangle ABН, the angle ABН = (135 – 90) = 45, then the legs of the triangle are equal, AH = BH = X cm. Let’s draw the height of the CК. Since the trapezoid is isosceles, then DK = AH = X cm.

Then the length of the segment НК = АD – АН – DК = 3 * X – X – X = X.

Quadrangle HBCК is a rectangle, then NC = X = 6 cm.

BH = 6 cm, AD = 3 * 6 = 18 cm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * ВН / 2 = (6 + 18) * 6/2 = 72 cm2.

Answer: The area of the trapezoid is 72 cm2.