Examine the diagram of $ABCD$ at right.  

1. If opposite sides of the quadrilateral are parallel and all sides are congruent, what type of quadrilateral is $ABCD$?

   Hint (a):

   Think about the requirements for different shapes. What shape has these requirements?

2. List what you know about the diagonals of $ABCD$.

   Hint (b):

   Look at the diagram. What do these lines do?

   Answer (b):

   They are perpendicular and intersect each other at their midpoints. They also bisect the angles of the quadrilateral.

3. Find the area of $ABCD$ if $BC = 8$ and $m∠ABC = 60°$.

   Hint (c):

   Find the area of one of the triangles, then find the total area. What do you know about the triangles that can help you?

   Step 1(c):

   The angles at the center are $90°$, so it is a $30°\text{-}60°\text{-}90°$ triangle.

   The length from the angle to the center is $4\sqrt{3}$.

   Step 2(c):

   Triangle: $\frac{1}{2}(4)(4\sqrt{3})=8\sqrt{3}$

   Step 3(c):

   Total Area: $4(8\sqrt{3})$

   Answer (c):

   $55.4\text{ units}^2$