To find the total area of the composite shape made of a rectangle and two triangles, we first need to calculate the area of each component separately.
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Area of the Rectangle: The formula for the area of a rectangle is: \[ \text{Area} = \text{length} \times \text{width} \] Given that the rectangle is 9 cm long and 3 cm wide: \[ \text{Area of Rectangle} = 9 , \text{cm} \times 3 , \text{cm} = 27 , \text{square centimeters} \]
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Area of the Triangles: Each triangle is a right triangle with a base of 2 cm and a height of 3 cm (the height of the rectangle). The area of a right triangle is given by: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] For one triangle: \[ \text{Area of one triangle} = \frac{1}{2} \times 2 , \text{cm} \times 3 , \text{cm} = 3 , \text{square centimeters} \]
Since there are two triangles: \[ \text{Area of two triangles} = 2 \times 3 , \text{square centimeters} = 6 , \text{square centimeters} \]
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Total Area of the Composite Shape: Now we can find the total area by adding the areas of the rectangle and the triangles: \[ \text{Total Area} = \text{Area of Rectangle} + \text{Area of two triangles} = 27 , \text{cm}^2 + 6 , \text{cm}^2 = 33 , \text{square centimeters} \]
Thus, the total area of the piece of jewelry is 33 square centimeters.