Question

A, B, C and D lie on a circle, centre O, radius 8 cm.

AB and CD are tangents to a circle, centre O, radius 4 cm.

ABCD is a rectangle.

( b ) Calculate the shaded area

Answer 1

To calculate the shaded area, we need to find the area of the rectangle ABCD and subtract the area of the circle with radius 4 cm.

The area of the rectangle ABCD is given by:

Area of rectangle = length x width
Area of rectangle = 2(8 cm) x 2(4 cm)
Area of rectangle = 32 cm x 8 cm
Area of rectangle = 256 cm^2

The area of the circle with radius 4 cm is given by:

Area of circle = πr^2
Area of circle = π(4 cm)^2
Area of circle = π(16 cm)
Area of circle ≈ 50.24 cm^2

Therefore, the shaded area is:

Shaded area = Area of rectangle - Area of circle
Shaded area = 256 cm^2 - 50.24 cm^2
Shaded area ≈ 205.76 cm^2

So, the shaded area is approximately 205.76 cm^2.