Hector designs the piece of jewelry shown below. All lengths are marked in centimeters. What is the total area of the piece of jewelry?

(1 point)
Responses

30 square centimeters
30 square centimeters

39 square centimeters 
39 square centimeters 

33 square centimeters
33 square centimeters

27 square centimeters

The image shows three shapes.

1. Shape: triangle
Bottom: 2
Side: 3

2. Shape: rectangle
Bottom: 9
Side: 3

3. Shape: triangle
Bottom: 2
Side: 3

1 answer

To calculate the total area of the piece of jewelry, we will find the area of each shape and then add them together.

  1. 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

    \[ \text{Area} = \frac{1}{2} \times 2 \times 3 = 3 \text{ square centimeters} \]

  2. 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

    \[ \text{Area} = 9 \times 3 = 27 \text{ square centimeters} \]

  3. 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.