Question

Hector designs three piece's of jewelry described below. All lengths are marked in centimeters. What is the total area of all the pieces combined together of the jewelry?
Triangle jewelry:
Bottom base: 2 cm
Side base: 3 cm
Height: 3 cm.
Rectangle jewelry:
Width: 9 cm
Height: 3 cm

Answer 1

To find the total area of the three pieces of jewelry, we need to calculate the area of each piece separately and then add them together.

### 1. Area of the Triangle
The formula for the area of a triangle is:

\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

Given:
- Base = 2 cm (we will use the bottom base)
- Height = 3 cm

Calculating the area:

\[
\text{Area} = \frac{1}{2} \times 2 \times 3 = \frac{1}{2} \times 6 = 3 \text{ cm}^2
\]

### 2. Area of the Rectangle
The formula for the area of a rectangle is:

\[
\text{Area} = \text{width} \times \text{height}
\]

Given:
- Width = 9 cm
- Height = 3 cm

Calculating the area:

\[
\text{Area} = 9 \times 3 = 27 \text{ cm}^2
\]

### Total Area
Now we add the areas of the triangle and the rectangle together:

\[
\text{Total Area} = \text{Area of Triangle} + \text{Area of Rectangle} = 3 \text{ cm}^2 + 27 \text{ cm}^2 = 30 \text{ cm}^2
\]

Thus, the total area of all the pieces combined together is:

\[
\boxed{30 \text{ cm}^2}
\]