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.