The shape ABCDOA, as shown in Figure 1, consists of a sector COD of a circle centre O joined to a sector AOB of a different circle, also centre O - Edexcel - A-Level Maths Pure - Question 3 - 2017 - Paper 1

To find the area of the shaded sector AOB, we first need the angle $\angle AOB$ which can be derived from:

$\angle AOB = \pi - \angle COD = \pi - 0.4 \text{ radians} \approx 2.74 \text{ radians}$

Using the formula for the area of a sector:

$\text{Area} = \frac{1}{2} r^2 \theta$

We have:

• $r$ is the radius of sector AOB, calculated as $12 - 7.5 = 4.5$ cm.
• $\theta = 2.74$ radians.

Substituting these values gives:

$\text{Area} = \frac{1}{2} (4.5)^2 (2.74)\approx 27.8 \text{ cm}^2$

Thus, the area of the shaded sector AOB is approximately 27.8 cm².