All four corners of a rectangle are on the circumference of a circle.
The rectangle has a perimeter of 24 cm.
The ratio of length : width for the rectangle is 3 : 1
What is the area of the shaded region in cm2 ?

Answer:

12) F

It is important for you to realise that the diameter of the circle is the diagonal of the rectangle.

Let width of rectangle be W. So length is 3W

2(3W + W) = 24 cm
8W = 24 cm
W = 3 cm
Length = 3 x 3 = 9 cm

Diagonal = hypotenuse of one right-angled triangle.
Diagonal² = 3² + 9²
Diagonal² = 9 + 81
Diagonal² = 90
Diagonal = 3√10
Radius = (3√10 ÷ 2) cm

Area of circle = π (3√10 ÷ 2) ² = ⁹⁰/₄ cm²
Area of rectangle = 9 x 3 = 27 cm²
Area of shaded area = (⁹⁰/₄) π – 27 cm² 

Obviously, this is not one of the options. However, F is the same as the answer. So F is correct.