Question

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

39 square centimeters 
39 square centimeters 

33 square centimeters
33 square centimeters

27 square centimeters

The image shows three shapes.

1. Shape: triangle
Bottom: 2
Side: 3

2. Shape: rectangle
Bottom: 9
Side: 2

3. Shape: triangle
Bottom: 2
Side: 3

Answer 1

To find the total area of the piece of jewelry consisting of the two triangles and one rectangle, we can calculate the area of each shape separately and then sum them up.

1. **Area of Triangle (Base = 2 cm, Height = 3 cm):**
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 2 \times 3 = \frac{6}{2} = 3 \text{ square centimeters}
\]

2. **Area of Rectangle (Length = 9 cm, Width = 2 cm):**
\[
\text{Area}_{\text{rectangle}} = \text{Length} \times \text{Width} = 9 \times 2 = 18 \text{ square centimeters}
\]

3. **Area of Triangle (Base = 2 cm, Height = 3 cm):**
(This is the same calculation as the first triangle)
\[
\text{Area}_{\text{triangle}} = 3 \text{ square centimeters}
\]

Now, let's sum the areas of all three shapes:
\[
\text{Total Area} = \text{Area}_{\text{triangle1}} + \text{Area}_{\text{rectangle}} + \text{Area}_{\text{triangle2}} = 3 + 18 + 3 = 24 \text{ square centimeters}
\]

It looks like we should double-check the second triangle again or the calculations in case something is mismatched with area expectations.

### Review:
1. **Triangle 1 Area: 3 cm²**
2. **Rectangle Area: 18 cm²**
3. **Triangle 2 Area: 3 cm²**

Notably, I'm getting 24 cm². If we need to find options:

So **none of the initially checked choices (27, 30, 33, 39) actually appear correct here by a standard calculation**. It might be a contextual detail missing on how shapes overlap, or if they’re considering part of intersections or other dimensions in other shapes.

In general practice, you need to re-evaluate or confirm the total as **24 cm² (or review context checks on other conditions present).**