Question

A quadrilateral 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?

Answer 1

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
`√(3)`*6. The sum or the total area is equal to 127.18 cm2.