The diagram shows a regular decagon (ten-sided shape with all sides equal and all interior angles equal) - HSC - SSCE Mathematics Standard - Question 32 - 2020 - Paper 1

The interior angle of a regular decagon can be calculated as:

$\angle AOB = \frac{360^\circ}{10} = 36^\circ.$

Using the sine rule in triangle OAB:

$\sin(72^\circ) = \frac{8}{r}$

From this, we can rearrange to find r:

$r = \frac{8}{\sin(72^\circ)}.$

Calculating the value gives us:

$r \approx 12.944\,cm.$

The area of triangle OAB can be calculated as follows:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8 \times r \times \sin(36^\circ).$

After substituting the values:

$\text{Area} = 10 \times \frac{1}{2} \times (12.944\ldots)^2 \times \sin(36^\circ) \approx 492.4\, cm^2.$

Thus, the area of the ten-sided shape is approximately 492.4 cm².