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To solve this problem, we need to calculate the surface area of the prism in order to determine how much glitter Leon will need.

### Step 1: Identify the shape of the prism.
The prism appears to have a triangular base, and we are given the following dimensions:
- The two slant heights of the triangle: $ 19 \, \text{m} $ and $ 27 \, \text{m} $
- The height of the triangular face: $ 10 \, \text{m} $
- The base of the triangular face: $ 23 \, \text{m} $
- The length of the prism: $ 12 \, \text{m} $

### Step 2: Calculate the area of the triangular faces.
The area of a triangle is given by the formula:
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}
\]
For the triangular faces:
\[
\text{Area of triangular face} = \frac{1}{2} \times 23 \, \text{m} \times 10 \, \text{m} = 115 \, \text{m}^2
\]
Since there are two triangular faces (front and back), the total area of the triangular faces is:
\[
\text{Total area of triangular faces} = 115 \, \text{m}^2 \times 2 = 230 \, \text{m}^2
\]

### Step 3: Calculate the area of the rectangular faces.
Each side of the prism is a rectangle, and we can calculate the area of each of the three rectangular faces:
- One rectangular face has dimensions $ 23 \, \text{m} \times 12 \, \text{m} $, so:
\[
\text{Area of first rectangular face} = 23 \times 12 = 276 \, \text{m}^2
\]
- The other two rectangular faces have dimensions of $ 27 \, \text{m} \times 12 \, \text{m} $ and $ 19 \, \text{m} \times 12 \, \text{m} $, so:
\[
\text{Area of second rectangular face} = 27 \times 12 = 324 \, \text{m}^2
\]
\[
\text{Area of third rectangular face} = 19 \times 12 = 228 \, \text{m}^2
\]

### Step 4: Calculate the total surface area.
Now, sum the areas of all the faces:
\[
\text{Total surface area} = 230 \, \text{m}^2 + 276 \, \text{m}^2 + 324 \, \text{m}^2 + 228 \, \text{m}^2
\]
\[
\text{Total surface area} = 1058 \, \text{m}^2
\]

### Step 5: Calculate the amount of glitter needed.
Since 70 grams of glitter are needed for each square meter:
\[
\text{Total glitter} = 70 \, \text{g/m}^2 \times 1058 \, \text{m}^2 = 74060 \, \text{g}
\]
Thus, Leon will need **74.06 kg** of glitter to cover the prism.

Would you like more details on any step or have any other questions?

Here are 5 related questions to deepen your understanding:
1. How would the glitter requirement change if the base of the triangular face was doubled?
2. What is the total cost if glitter costs $5 per kilogram?
3. How would you calculate the volume of this triangular prism?
4. What happens if the height of the triangular face increases by 5 meters?
5. How can we generalize the glitter formula for any prism?

**Tip:** Always double-check your units when calculating area and volume to avoid mistakes!

Leon wants to cover a triangular prism in glitter. If 70 g of glitter is needed to cover each m², how much glitter will he need to cover the prism completely?

Learn how to calculate the amount of glitter needed to cover a triangular prism with a surface area of 1058 m², given that 70g of glitter is required per square meter. This problem involves key geometric concepts like the surface area of prisms and triangles. Suitable for Grades 7-9.

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