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
27 square centimeters
27 square centimeters
30 square centimeters
30 square centimeters
39 square centimeters
39 square centimeters
33 square centimeters
The total area of the piece of jewelry can be calculated by splitting it into three separate shapes: a rectangle, a triangle, and a semi-circle.
Area of the rectangle = 3 x 6 = 18 square centimeters
Area of the triangle = 1/2 x 3 x 6 = 9 square centimeters
Area of the semi-circle = 1/2 x π x 3^2 = 4.5π square centimeters
Adding all the areas together:
18 + 9 + 4.5π ≈ 18 + 9 + 14.13 ≈ 41.13 square centimeters
Therefore, the closest option is 39 square centimeters.