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

33 square centimeters
33 square centimeters

27 square centimeters
27 square centimeters

30 square centimeters
30 square centimeters

39 square centimeters
39 square centimeters

Answer 1

To find the total area of the composite shape that includes a rectangle and two triangles, we can calculate the area of each individual part and then sum them up.

1. **Area of the Rectangle:**
The area \(A\) of a rectangle is given by the formula:
\[
A = \text{length} \times \text{width}
\]
For the given rectangle:
- Length = 9 cm
- Width = 3 cm
\[
A_{\text{rectangle}} = 9 \times 3 = 27 \text{ square centimeters}
\]

2. **Area of the Triangles:**
Each triangle is a right triangle with a base and height of 2 cm.
The area \(A\) of a right triangle is given by the formula:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
For each triangle:
- Base = 2 cm
- Height = 3 cm (since the triangle's height extends from the rectangle's side)
\[
A_{\text{triangle}} = \frac{1}{2} \times 2 \times 3 = 3 \text{ square centimeters}
\]

Since there are two triangles:
\[
A_{\text{total triangles}} = 3 + 3 = 6 \text{ square centimeters}
\]

3. **Total Area:**
Now, we add the area of the rectangle to the total area of the triangles:
\[
A_{\text{total}} = A_{\text{rectangle}} + A_{\text{total triangles}} = 27 + 6 = 33 \text{ square centimeters}
\]

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