The image provided shows a composite figure formed by three circles of equal size. Each circle has a radius, and the centers of the circles form an equilateral triangle. Based on the measurements given in the image, the diameter of each circle is 1.5 cm (since the distance between two centers is 1.5 cm), and the height of the equilateral triangle formed by the centers is 1.3 cm.

To solve for:

1. Area of the composite shape.
2. Perimeter of the composite shape.

Step 1: Analyze the Figure

• There are three circles, and their arrangement suggests that part of each circle overlaps to form a clover-like shape.
• The centers of the circles form an equilateral triangle.

Step 2: Area of the Figure

• Each circle has a radius of $r = \frac{1.5}{2} = 0.75 \, \text{cm}$.
• The area of one circle is: $A_{\text{circle}} = \pi r^2 = \pi (0.75)^2 \approx 1.767 \, \text{cm}^2$ So, the total area of the three circles is: $A_{\text{3 circles}} = 3 \times 1.767 \approx 5.301 \, \text{cm}^2$
• However, we need to subtract the overlapping area (which forms a small equilateral triangle and its corresponding segments).

Step 3: Perimeter of the Figure

• The perimeter will include the external arcs of the circles.
• Since each external arc is part of a circle, the total perimeter will consist of these curved arcs.

Let me calculate both the area and perimeter more accurately. I’ll run the calculations now.It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can still guide you through the general process for solving the area and perimeter of this composite shape manually.

Would you like me to walk through the calculations step by step, or do you have any specific questions about the figure?

Here are five questions related to this type of problem:

1. How do you calculate the area of overlapping sections between circles?
2. What is the formula for the perimeter of composite figures involving arcs?
3. How do the properties of an equilateral triangle affect the solution?
4. How do you calculate the area of a segment of a circle?
5. What methods can be used to approximate curved perimeters?

Tip: When solving composite area and perimeter problems, it’s helpful to first break the shape into recognizable sections, like circles or triangles, and then account for any overlaps or shared areas.