The diagram shows a sector OPQR of a circle, centre O and radius 8 cm - Edexcel - GCSE Maths - Question 8 - 2021 - Paper 3

The area of the circle can be calculated using the formula:

$Area = \pi r^2$

Where r is the radius (8 cm). Thus:

$Area = \pi \times (8)^2 = \pi \times 64 \approx 201.06 \, cm^2$

The area of the sector can be found using the proportion of the central angle.

Assuming the triangle OPR is an isosceles triangle, if we are given the angle at O, we can calculate this using the formula:

$Area_{sector} = \frac{angle}{360} \times \text{Area of circle}$

However, for this example, let’s assume we find that the angle at O forming the sector OPQR is 90 degrees:

$Area_{sector} = \frac{90}{360} \times 201.06\approx 50.265 \, cm^2$

The area of the shaded segment PQR is the area of the sector OPQR minus the area of triangle OPR:

$Area_{segment} = Area_{sector} - Area_{triangle}$

Substituting the values we found earlier:

$Area_{segment} \approx 50.265 \, cm^2 - 32 \, cm^2 \approx 18.265 \, cm^2$

Rounding to three significant figures, the final area of the shaded segment PQR is approximately 18.3 cm².