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)
Responses
30 square centimeters
30 square centimeters
27 square centimeters
27 square centimeters
39 square centimeters
39 square centimeters
33 square centimeters
33 square centimeters
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27 square centimeters
To find the total area of the piece of jewelry, we first calculate the individual areas of the rectangle and the two triangles, and then add them up.
Rectangle area = length x width = 9 cm x 3 cm = 27 square cm
Triangle area = (base x height)/2
For the triangle on the left:
Triangle area = (3 cm x 3 cm)/2 = 4.5 square cm
For the triangle on the right:
Triangle area = (2 cm x 3 cm)/2 = 3 square cm
Total area = 27 square cm + 4.5 square cm + 3 square cm = 27 square cm
So, the total area of the piece of jewelry is 27 square centimeters.