Let's begin with recalling the 30^(∘)-60^(∘)-90^(∘) Triangle Theorem. This theorem tells us that the length of the hypotenuse of this right triangle is 2 times the length of the shorter leg s, and the length of the longer leg is sqrt(3) times the length of the shorter leg.
Now let's take a look at the given picture.
Since we are given that the longer leg of â–³ AED is 4sqrt(3), we know that the shorter leg of this triangle has a length of 4 and the hypotenuse will have a length of 2(4)=8.
We found that the side length of square ABCD is 8. To evaluate the area of this figure, let's recall that the area of a square is the square of its side length.
A_(ABCD)=8^2=64
The area of square ABCD is 64 square units. This corresponds with answer C.
