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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
33 square centimeters
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1 answer

To calculate the total area of the composite shape, we need to find the area of the rectangle and the two triangles.

  1. Area of the Rectangle

    • Length = 9 cm
    • Width = 3 cm
    • Area = Length × Width = 9 cm × 3 cm = 27 square centimeters

  2. Area of the Triangles

    • Each triangle has a base of 2 cm and a height of 3 cm.

    For the triangles:

    • Area of one triangle = (1/2) × base × height = (1/2) × 2 cm × 3 cm = 3 square centimeters

    Since there are two triangles:

    • Total area of the triangles = 3 cm + 3 cm = 6 square centimeters

  3. Total Area of the Composite Shape

    • Total Area = Area of Rectangle + Total Area of Triangles
    • Total Area = 27 cm² + 6 cm² = 33 square centimeters

Therefore, the total area of the piece of jewelry is 33 square centimeters.