Use the image to answer the question.
A composite shape is drawn using a rectangle and 2 triangles. A horizontally aligned rectangle is 9 centimeters long and 3 centimeters wide. A right triangle facing upward adjoins the rectangle on the left side marked 3 centimeters. A right triangle facing downward adjoins the rectangle on the right side. The base leg of both triangles measures 2 centimeters.
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)
33 square centimeters
27 square centimeters
30 square centimeters
39 square centimeters
To find the total area of the piece of jewelry, we need to find the individual areas of the rectangle and both triangles and then add them together.
Rectangle area = length x width
Rectangle area = 9 cm x 3 cm
Rectangle area = 27 square cm
Triangle area = 1/2 x base x height
Triangle area = 1/2 x 3 cm x 3 cm
Triangle area = 4.5 square cm each
Total area = Rectangle area + 2(Triangle area)
Total area = 27 square cm + 2(4.5 square cm)
Total area = 27 square cm + 9 square cm
Total area = 36 square cm
Therefore, the total area of the piece of jewelry is 36 square centimeters. None of the provided options are correct, but the closest is 39 square centimeters.