To find the total area of the composite shape described, we need to calculate the area of the rectangle and the areas of the two triangles separately before summing them up.
-
Area of the rectangle: The formula for the area of a rectangle is: \[ \text{Area} = \text{length} \times \text{width} \] Given the length is 9 cm and the width is 3 cm: \[ \text{Area}_{\text{rectangle}} = 9 , \text{cm} \times 3 , \text{cm} = 27 , \text{cm}^2 \]
-
Area of each triangle: The formula for the area of a triangle is: \[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \] Each triangle has a base of 2 cm and a height of 3 cm (since they are both right triangles adjoining the rectangle). Thus, the area for one triangle is: \[ \text{Area}_{\text{triangle}} = \frac{1}{2} \times 2 , \text{cm} \times 3 , \text{cm} = \frac{1}{2} \times 6 , \text{cm}^2 = 3 , \text{cm}^2 \]
Since there are two triangles, the total area of the triangles is: \[ \text{Total area}_{\text{triangles}} = 2 \times 3 , \text{cm}^2 = 6 , \text{cm}^2 \]
-
Total area of the piece of jewelry: Now we add the area of the rectangle and the total area of the triangles: \[ \text{Total area} = \text{Area}{\text{rectangle}} + \text{Total area}{\text{triangles}} = 27 , \text{cm}^2 + 6 , \text{cm}^2 = 33 , \text{cm}^2 \]
Therefore, the total area of the piece of jewelry is 33 square centimeters. So, the correct answer is:
33 square centimeters.