Final answer:
The perimeter of the sector-shaped pendant is calculated by adding the length of the arc to twice the radius. The perimeter calculation yields approximately 18.89 cm, but this does not match any of the provided options, indicating an issue with the calculation or choices.
Step-by-step explanation:
The perimeter of a pendant in the shape of a sector of a circle with a 40-degree central angle and a 7 cm radius can be calculated by adding the length of the two radii to the length of the arc.
The formula for the arc length (L) of a circle with radius (r) and central angle (θ in degrees) is L = θ/360 × 2πr.
For this pendant, we substitute θ = 40 degrees and r = 7 cm into the formula to get:
L = 40/360 × 2π × 7 = (1/9) × 2π × 7 ≈ 4.8869 cm
Add the lengths of the two radii (2 × 7 cm) to get the total perimeter:
Perimeter = 2r + L = 2 × 7 + 4.8869 cm ≈ 18.8869 cm
However, the options provided in the question do not include this value, which suggests there might be an error in either the calculation or the given choices.