A quadrilateral contains two equal sides measuring 12 cm each with an included right angle. If the measure of the third side is 8 cm and the angle opposite the right angle is 120 degrees, find the fourth side and the area of the quadrilateral.

Answer 1

As usual, draw a figure. If we start at the right angle and label the vertices clockwise, then we see that BD is the hypotenuse of an isosceles right triangle, with length 12√2.

If the 4th side is x, then we have from the law of cosines,

(12√2)^2 = 8^2 + x^2 - 2(8)(x)cos120°
or,
x^2 + 8x - 224 = 0
x = 4(√15-1) = 11.5

Now you can split the area into a rectangle and two triangles and find the area.

Answer 2

d^4=100/6