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
33 square centimeters
33 square centimeters
30 square centimeters
30 square centimeters
39 square centimeters
39 square centimeters
27 square centimeters
To find the total area of the piece of jewelry, we need to calculate the area of the rectangle and add the areas of the two triangles.
Rectangle:
Length = 9 cm, Width = 3 cm
Area = Length x Width
Area = 9 cm x 3 cm = 27 square cm
Triangles:
For the triangle on the left:
Base = 3 cm, Height = 3 cm
Area = 0.5 x Base x Height
Area = 0.5 x 3 cm x 3 cm = 4.5 square cm
For the triangle on the right:
Base = 2 cm, Height = 3 cm
Area = 0.5 x Base x Height
Area = 0.5 x 2 cm x 3 cm = 3 square cm
Total area = Area of Rectangle + Area of Left Triangle + Area of Right Triangle
Total area = 27 square cm + 4.5 square cm + 3 square cm
Total area = 34.5 square cm
Therefore, the total area of the piece of jewelry is 34.5 square centimeters. None of the given options match exactly, but the closest one is 33 square centimeters.