A semicircle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular

Geometry

A semicircle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn meeting the circumference of the semi-circle at D. Given that AC = 2 cm and CD = 6 cm, the area of the semicircle (in sq. cm) will be:

  1. 32 π
  2. 40.5 π
  3. 50 π
  4. 81 π

Answer

Angle in a semi-circle is a right angle.

∠ADC = 90°

CD2 = AC × CB

AC = 2 cm and CD = 6 cm

CB = 18 cm

Hence, AB = AC + CB = 20 cm

Radius of semicircle = 10 cm

Area of semi-circle = 1/2 * π * r2 = 50 π

The correct option is C.