Question

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

39 square centimeters
39 square centimeters

33 square centimeters
33 square centimeters

30 square centimeters
30 square centimeters

27 square centimeters
27 square centimeters
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Answer 1

To find the total area of the composite shape in question, we need to calculate the areas of the rectangle and the two triangles separately and then add them together.

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 height of 3 cm and a base of 2 cm. Since there are two triangles (one facing upwards and one facing downwards), we'll calculate the area for one triangle and then double it.
   • 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 both triangles = 2 × 3 square centimeters = 6 square centimeters

3. Total area of the composite shape:

   • Total area = Area of rectangle + Total area of triangles
   • Total area = 27 square centimeters + 6 square centimeters = 33 square centimeters

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