AJWILL wrote: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.
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