Final answer:
The area of Circle A tangent to two parallel lines and two other circles can be found by summing the radii of the other circles to find its radius, then applying the area formula A = πr².
Step-by-step explanation:
To find the area of Circle A that is tangent to two parallel lines and tangent to Circle B with r=9cm and Circle C with r=16cm, we need to understand the relationships between the circles and use the formula for the area of a circle, A = πr².
Since Circle B and Circle C are tangent to each other and Circle A is tangent to both circles and the two parallel lines, we can deduce that the radius of Circle A will be the sum of the radii of Circles B and C, giving us a radius for Circle A of r=25cm (9cm + 16cm). The formula for the area of a circle is A = πr², therefore:
A = π(25cm)²
A = π625π cm²
The exact area can be left in terms of π for a more precise result or calculated using a numerical approximation of π (3.14159) if a decimal answer is required.