Question 697587
The formula for the area of a parallelogram is: A = b*h. The base in these area formulas can be any side of the polygon. Since all the sides of this polygon are 4's then we know our base will be 4.<br>
The hard part is the height. If you draw a diagram of what you describe then you will see that an equilateral triangle with sides of 4 is formed by two sides of the parallelogram (rhombus actually) and the diagonal whose length is 4. The height of this triangle will also be the height of the parallelogram.<br>
The angles in all equilateral triangles are always 60 degrees. If we draw in the height for the triangle we will have a 30-60-90 right triangle with a hypotenuse of 4. From Trigonometry or from remembering the relationships between the sides of 30-60-90 triangles we should be able to figure out that height is {{{2sqrt(3)}}}<br>
So the area of this parallelogram will be:
{{{A = b*h = 4*2sqrt(3) = 8sqrt(3)}}}