Use the image to answer the question.

Question

9 cm
2 cm
3 cm
2 cm
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)
• 30 square centimeters
• 33 square centimeters
• 39 square centimeters
• 27 square centimeters

Answer 1

To calculate the total area of the piece of jewelry, we need to find the area of each individual section and then add them together.

Area of the rectangle on the left:
9 cm x 2 cm = 18 square centimeters

Area of the rectangle on the bottom:
3 cm x 2 cm = 6 square centimeters

Area of the rectangle on the right:
9 cm x 2 cm = 18 square centimeters

Total area:
18 square centimeters + 6 square centimeters + 18 square centimeters = 42 square centimeters

Therefore, the total area of the piece of jewelry is 42 square centimeters.
Since this answer isn't one of the multiple choice options, let's try a different approach:

We can see that the total area of the piece of jewelry is equal to:
9 cm x 2 cm = 18 square centimeters for the larger rectangle in the center

And on the right and left sides, we see that there are equal areas.
Let's calculate the total area for just one of the sides:
3 cm x 2 cm = 6 square centimeters for the smaller rectangle on the bottom
9 cm x 2 cm = 18 square centimeters for the taller rectangle on the side
Therefore, the total area for one side is 6 + 18 = 24 square centimeters

Since we have two sides with symmetrical areas, we can add this two times for the sides and once for the larger rectangle to get the total area:
24 square centimeters (side) + 18 square centimeters (center) = 42 square centimeters

Therefore, the correct total area of the piece of jewelry would be 42 square centimeters.