Area of a Geometric Flower: Solving with Variables 2x, 1.2x, and 1.5x

To solve this problem, we'll calculate the areas of the different circles and then add them accordingly. This approach requires determining each circle's area as follows:

• Identify the radii of the circles given as $2x$, $1.5x$, $1.2x$, constants like 3, and 2.
• Use the circle area formula $A = \pi r^2$ to calculate each circle's area.
• Add all these areas to determine the total area of the flower shape.

Let's begin:

First Circle: Radius $= 2x$
Area $= \pi (2x)^2 = 4x^2\pi$

Second Circle: Radius $= 1.5x$
Area $= \pi (1.5x)^2 = 2.25x^2\pi$

Third Circle: Radius $= 1.2x$
Area $= \pi (1.2x)^2 = 1.44x^2\pi$

Fourth Circle: Radius $= 3$
Area $= \pi (3)^2 = 9\pi$

Fifth Circle: Radius $= 2$
Area $= \pi (2)^2 = 4\pi$

Now, summing the areas in terms of $\pi$, we find:

Total Area $= 4x^2\pi + 2.25x^2\pi + 1.44x^2\pi + 9\pi + 4\pi$
Combine like terms:
Total Area $= (4 + 2.25 + 1.44)x^2\pi + (9 + 4)\pi$

Total Area $= 7.69x^2\pi + 13\pi$

Therefore, the area of the flower depicted in the diagram is $7.69x^2\pi+13\pi$.