Question

Help!!Medal will be given

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 the right angle is 120 degrees. find the measurement of the fourth side and the area of the quadrilateral

Answer 1

Draw it:

Make a-b-c be right angle with sides 12cm long and 90deg between them.

Make d be point that is somewhere between a and c but 8cm from c.

Distance abc is right angle triangle with hypotenuse ac=12*sqrt(2).

Then using cosine law we find missing side. note that there will be two solutions:

b^2 = a^2 + c^2 - 2ac*cos(120)