To solve the problem in the image, we need to calculate the surface area of the prism and then determine how much glitter is required based on the information given.

Step 1: Surface area of the prism

The shape is a triangular prism. The surface area of a triangular prism consists of:

• Two triangular bases
• Three rectangular faces

Triangular base:

• The base of the triangle is 23 m, and the height is 10 m. The area $A$ of a triangle is given by:

$A = \frac{1}{2} \times \text{base} \times \text{height}$

So the area of one triangular base is:

$A = \frac{1}{2} \times 23 \times 10 = 115 \, \text{m}^2$

Since there are two triangular bases, the total area of the two bases is:

$2 \times 115 = 230 \, \text{m}^2$

Rectangular faces:

• One rectangular face has dimensions $23 \, \text{m} \times 27 \, \text{m}$, so its area is:

$23 \times 27 = 621 \, \text{m}^2$

• The second rectangular face has dimensions $19 \, \text{m} \times 27 \, \text{m}$, so its area is:

$19 \times 27 = 513 \, \text{m}^2$

• The third rectangular face has dimensions $12 \, \text{m} \times 27 \, \text{m}$, so its area is:

$12 \times 27 = 324 \, \text{m}^2$

Total surface area:

Now, summing up all the areas:

$230 + 621 + 513 + 324 = 1688 \, \text{m}^2$

Step 2: Glitter required

Given that 70 grams of glitter are needed per square meter, the total amount of glitter required is:

$1688 \, \text{m}^2 \times 70 \, \text{g/m}^2 = 118,160 \, \text{g}$

Thus, Leon will need 118,160 grams (or 118.16 kilograms) of glitter to cover the prism completely.

Would you like any further details or clarifications?

Here are 5 follow-up questions for you:

1. What would be the effect if the glitter coverage per square meter increased?
2. Can you calculate the volume of the prism?
3. What would happen if the dimensions of the triangular base changed?
4. How does the surface area relate to the volume of a prism?
5. Can you generalize the formula for the surface area of any triangular prism?

Tip: When calculating the surface area of a prism, remember that the two triangular bases are always congruent.