Asked by AJ
Problem:
ABCDE$\ is an equilateral pentagon with side length 2 in which angle B= angle E=120 degrees. The area of ABCDE can be expressed in the form square root of x + square root of y for some integers x and y. Find x+y.
I don't understand. I really need help.
ABCDE$\ 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.
Answers
Answered by
Steve
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.
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.
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