Find the area of an isosceles trapezoid if its obtuse angle is 135, and the bases are 5 cm and 13 cm.

Since the desired trapezoid is isosceles, its base angles are equal, as are the obtuse angles. Therefore, the angle at the base will be equal to:

180o – 135 o = 45 o.

T. to. tg 45 o = 1, then the height of the trapezoid will be equal to half the height of the lower base over the upper one:

h = (13 – 5) / 2 = 8/2 = 4 (cm).

Recall that the area of a trapezoid is determined by the formula:

S = ((a + b) / 2) * h,

where a and b are bases,

h – height.

Then the area will be equal to:

S = ((5 + 13) / 2) * 4 = 9 * 4 = 36 (cm 2).

Answer: 36 cm 2.