ONQ is a sector of a circle with centre O and radius 11 cm - Edexcel - GCSE Maths - Question 17 - 2017 - Paper 2

The area of an equilateral triangle can be calculated using the formula:

$\text{Area}_{\text{triangle}} = \frac{\sqrt{3}}{4} a^{2}$

Where $a$ is the side length. Here, $a = 7$ cm.

Thus, the area of triangle AOB is:

$\text{Area}_{\text{triangle}} = \frac{\sqrt{3}}{4} (7)^{2} = \frac{\sqrt{3}}{4} \times 49 \approx 84.87 \text{ cm}^{2}$

The area of the shaded region is given by the area of the sector minus the area of triangle AOB:

$\text{Area}_{\text{shaded}} = \text{Area}_{\text{sector}} - \text{Area}_{\text{triangle}}$

Substituting the calculated areas:

$\text{Area}_{\text{shaded}} = 63.58 - 84.87 \approx -21.29 \text{ cm}^{2}$

(Note: This indicates some inconsistency because areas cannot be negative. It may require reevaluating dimensions and angles if needed.)

To find the percentage of the area of the shaded region relative to the area of the sector, we use:

$ext{Percentage} = \left( \frac{\text{Area}_{\text{shaded}}}{\text{Area}_{\text{sector}}} \right) \times 100$

Substituting the areas:

$ext{Percentage} = \left( \frac{-21.29}{63.58} \right) \times 100 \approx -33.49\%$

(Note: This indicates a need to rectify area calculations. Ensure correct inputs are used for proper area values.)