A cyclic quadrilateral has sides 5, 5, 12, 12 units. Find its area.

Since the cyclic quadrilateral has sides 5, 5, 12, 12, its semiperimeter is

$$s = \frac{5 + 5 + 12 + 12}{2}$$

$$= 17$$

For a cyclic quadrilateral, area is given by Brahmagupta formula:

$$\text{Area} = \sqrt{(s-a)(s-b)(s-c)(s-d)}$$

Substituting the values, we have:

$$\begin{aligned} \text{Area} &= \sqrt{(17-5)(17-5)(17-12)(17-12)} \\ &= \sqrt{(12)(12)(5)(5)} \\ &= \sqrt{3600} \\ &= 60 \end{aligned}$$

Hence, the area of the cyclic quadrilateral is 60 sq. units.