Aquadrilateral contains two equal sides measuring 12 cm each and an included right angle if the measure of the third side is 8 cm and the angle opposite to the right angle is 120 degrees. find the fourth side and the area of the quadrilateral?

The fourth side of the quadrilateral can be determined by taking the sin of the difference of 120 and 90 in which the expression becomes sin 30 = x/12 where x is the extra length difference from the third side. x is equal to 6. Hence the fourth side is equal to 8+6 or 14 cm. The area of the quadrialteral is the sum of the rectangle and the area of triangle. The area of the rectangle is 8*12 equal to 96 cm2.The area of teh triangle is .5*6*6. The sum or the total area is equal to 127.18 cm2.