please help.. geometary

[AJWILL]

In the figure given below, square ABCD is inscribed in a circle.Point E is joined to D and C such that AE = EB. If the area of the triangle is 20 square units find the difference in area of the circle and the square.

[neelgandham]

Let the side of the square be A and the radius of the circle be C.
i.e. AB = BC = CD = DA = A and AC = 2*C
We also know that AC is the diagonal of the square ABCD.
i.e. AC = 2*C = √2 * A => C = A/√2
Area of the Triangle DEC = (1/2)*Base*Height = (1/2) * CD * BC = (1/2)*A*A = 20 Square units
i.e. A*A = 40, A = 2√10 .
Radius of the circle = C = A/√2 = 2√10/√2 = 2√5.

Area of the circle = pi*C*C = pi*2√5*2√5 = pi*20 square units.
Area of the square = A*A = A*A = 40 square units.
Difference is areas = pi*20 - 40

[GMATGuruNY]

In the figure given below, square ABCD is inscribed in a circle.Point E is joined to D and C such that AE = EB. If the area of the triangle is 20 square units find the difference in area of the circle and the square.

Square:
The triangle and the square have the same base and height.
Since the area of a triangle = (1/2)bh and the area of a parallelogram = bh, the square is twice the size of the triangle.
Since the area of the triangle = 20, the area of the square = 2*20 = 40.

Circle:
The diameter of the circle is the diagonal of the square.
The diagonal of a square = s√2.
Since the area of the square is 40, s = √40 and d = (√40)(√2) = 4√5.
Thus, the radius of the circle = 2√5.
Area = �r² = �(2√5)² = 20�.

Circle - square = 20� - 40.

[pemdas]

there are 3 triangles which one's area is 20

anyways, it takes only 5 seconds to figure that area of square a^2 is the total of three triangles and the larger triangle is two times the area of each of the other two smaller triangles.

depending on the triangle's area (not specified here) we can get a^2=40 or a^2=80. Then a=sqrt(40) or sqrt(80). The radius of circle, R, would be 1/2*sqrt(2)*side of square ==> R=sqrt(2*40)/2 or sqrt(2*80)/2. The area of circle would be Pi*80/4 or Pi*160/4 ==> Pi*20 or Pi*40

We may get two answers depending on the triangle (not specified here): Pi*20-40 or Pi*40-80