To calculate the total area of the piece of jewelry, we will find the area of each shape and then add them together.
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Triangle: The formula for the area of a triangle is: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] For the first triangle:
- Base = 2 cm
- Height (side) = 3 cm
\[ \text{Area} = \frac{1}{2} \times 2 \times 3 = 3 \text{ square centimeters} \]
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Rectangle: The formula for the area of a rectangle is: \[ \text{Area} = \text{length} \times \text{width} \] For the rectangle:
- Length = 9 cm
- Width (side) = 3 cm
\[ \text{Area} = 9 \times 3 = 27 \text{ square centimeters} \]
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Triangle (again): For the second triangle, which is identical to the first:
- Base = 2 cm
- Height (side) = 3 cm
\[ \text{Area} = \frac{1}{2} \times 2 \times 3 = 3 \text{ square centimeters} \]
Now, we sum the areas of all shapes: \[ \text{Total Area} = 3 + 27 + 3 = 33 \text{ square centimeters} \]
Therefore, the total area of the piece of jewelry is 33 square centimeters.