Question

The given figures show a rectangle ABCD inscribed in a circle as shown alongside.
If AB = 28 cm and BC = 21 cm, find the area of the shaded portion of the given figure.

Answer 1

From the figure,
AB = 28 cm
BC = 21 cm

AC = `sqrt( "AB"^2 + "BC"^2 )`

= `sqrt( 28^2 + 21^2)` 

= 35.

Hence diameter of the circle is 35 cm and hence 
Area = π x `( 35/2 )^2` = 962.5 cm²

Area of the rectangle = 28 x 21 = 588 cm²

Hence area of the shaded portion is given by
A = 962 - 588 = 374.5 cm²