Problem:

Question

ABCDE$\ is an equilateral pentagon with side length 2 in which angle B= angle E=120 degrees. The area of ABCDE can be expressed in the form square root of x + square root of y for some integers x and y. Find x+y.

I don't understand. I really need help.

Answer 1

Draw diagonals AD and AC

Now you have two isosceles triangles AED and ABC with vertex angle 120° and equal sides of 2. Those can easily be solved.

Now triangle CAD is isosceles, with base CD=2 and the equal sides the base of the other two triangles.

Now just add up the areas of the three triangles.