OAC is a sector of a circle, centre O, radius 10 m - Edexcel - GCSE Maths - Question 20 - 2017 - Paper 2

We can use the base OC and the height AB of triangle ABC to find its area. The height AB can be determined using the tangent properties:

$AB = 10 \cdot \tan(60°) = 10 \cdot \sqrt{3} \approx 17.32 \, \text{m}$

The area of triangle ABC is given by:

$A = \frac{1}{2} \cdot \text{base} \cdot \text{height} = \frac{1}{2} \cdot OC \cdot AB = \frac{1}{2} \cdot 8.66 \cdot 17.32 \approx 74.99 \, \text{m}^2$

The area of the sector OAC is calculated using the formula:

$\text{Area} = \frac{\theta}{360°} \cdot \pi r^2$

where (\theta = 120°) and (r = 10 m). Thus,

$\text{Area}_{sector} = \frac{120}{360} \cdot \pi \cdot (10)^2 = \frac{1}{3} \cdot \pi \cdot 100\approx 104.72 \, \text{m}^2$

The shaded region is found by subtracting the area of triangle ABC from the area of the sector OAC:

$\text{Area}_{shaded} = \text{Area}_{sector} - \text{Area}_{triangle} \approx 104.72 - 74.99 = 29.73 \, \text{m}^2$

Thus, rounding to three significant figures, the area of the shaded region is: 29.7 m².