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 39 square centimeters 39 square centimeters 27 square centimeters 27 square centimeters 33 square centimeters 33 square centimeters 30 square centimeters
To find the total area of the piece of jewelry, we need to find the area of each individual shape and then add them together.
1. The rectangle:
Area = length × width = 10 cm × 4 cm = 40 square cm
2. The semicircle:
Area = (1/2) × πr^2 = (1/2) × π × (3 cm)^2 = (1/2) × π × 9 cm^2 = 4.5π square cm ≈ 14.13 square cm
3. The triangle:
Area = (1/2) × base × height = (1/2) × 3 cm × 6 cm = 9 square cm
Now, add the areas of the rectangle, semicircle, and triangle:
40 square cm + 14.13 square cm + 9 square cm = 63.13 square cm
Therefore, the total area of the piece of jewelry is approximately 63.13 square centimeters. None of the answer choices provided matches this result, so it appears that there might be an error in the measurements or calculations.