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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

33 square centimeters
33 square centimeters

27 square centimeters
27 square centimeters

39 square centimeters
39 square centimeters
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Answer 1

To find the total area of the composite shape consisting of the rectangle and the triangles, we need to calculate the area of each part separately and then sum them up.

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 is a right triangle with a base of 2 cm and a height of 3 cm.
   • 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 two triangles = 2 × 3 square centimeters = 6 square centimeters.

3. Total Area of the Composite Shape:

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

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

The correct response is: 33 square centimeters.