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
39 square centimeters
39 square centimeters
27 square centimeters
27 square centimeters
30 square centimeters
30 square centimeters
33 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:
Length = 9 cm
Width = 3 cm
Area of rectangle = Length x Width
Area of rectangle = 9 cm x 3 cm
Area of rectangle = 27 square cm
Triangles:
Height of triangles = 3 cm (for both)
Base of triangles = 2 cm (for both)
Area of one triangle = 1/2 x Base x Height
Area of one triangle = 1/2 x 2 cm x 3 cm
Area of one triangle = 3 square cm
Total area of both triangles = 3 square cm + 3 square cm = 6 square cm
Total area of the piece of jewelry = Area of rectangle + Total area of both triangles
Total area of the piece of jewelry = 27 square cm + 6 square cm
Total area of the piece of jewelry = 33 square cm
Therefore, the total area of the piece of jewelry is 33 square centimeters.