To find the total area of the composite shape, we can break it down into its components: the rectangle and the two triangles.
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Area of the rectangle: The area of a rectangle is given by the formula: \[ \text{Area} = \text{length} \times \text{width} \] Here, the length is 9 centimeters and the width is 3 centimeters. \[ \text{Area of the rectangle} = 9 , \text{cm} \times 3 , \text{cm} = 27 , \text{cm}^2 \]
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Area of each triangle: The area of a right triangle is given by the formula: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] Each triangle has a base of 2 centimeters and a height of 3 centimeters.
For one triangle: \[ \text{Area of one triangle} = \frac{1}{2} \times 2 , \text{cm} \times 3 , \text{cm} = \frac{1}{2} \times 6 , \text{cm}^2 = 3 , \text{cm}^2 \]
Since there are two triangles: \[ \text{Total area of the triangles} = 2 \times 3 , \text{cm}^2 = 6 , \text{cm}^2 \]
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Total area of the jewelry piece: Now we add the area of the rectangle and the areas of the triangles: \[ \text{Total area} = \text{Area of rectangle} + \text{Total area of triangles} \] \[ \text{Total area} = 27 , \text{cm}^2 + 6 , \text{cm}^2 = 33 , \text{cm}^2 \]
Thus, the total area of the piece of jewelry is 33 square centimeters.