Question
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
27 square centimeters
27 square centimeters
33 square centimeters
33 square centimeters
39 square centimeters
39 square centimeters
30 square centimeters
The total area of the piece of jewelry can be calculated by finding the area of the rectangle and adding the areas of the two triangles.
Area of rectangle = length x width = 9 cm x 3 cm = 27 square cm
Area of triangle = 1/2 x base x height
Area of first triangle = 1/2 x 3 cm x 3 cm = 4.5 square cm
Area of second triangle = 1/2 x 2 cm x 3 cm = 3 square cm
Total area = 27 square cm + 4.5 square cm + 3 square cm = 34.5 square cm
So, the total area of the piece of jewelry is 34.5 square centimeters.
Therefore, none of the options provided (27 square centimeters, 33 square centimeters, 39 square centimeters, 30 square centimeters) is correct.