Glitter Prism 87Fefe

1. **State the problem:** Katie wants to cover a triangular prism with glitter. Each square meter requires 60 g of glitter. We need to find the total amount of glitter required to cover the entire surface area of the prism. 2. **Identify the shape and dimensions:** The prism is triangular with base edges 13 m, 16 m, and 21 m, and a height (length) of the prism 25 m. The height of the triangle (not the prism) is 10 m. 3. **Calculate the area of the triangular base:** The base is a triangle with base $13$ m and height $10$ m. $$\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 13 \times 10 = 65 \text{ m}^2$$ 4. **Calculate the lateral surface area:** The prism has three rectangular faces corresponding to the three sides of the triangle, each with length $25$ m. - Side 1 area: $13 \times 25 = 325$ m² - Side 2 area: $16 \times 25 = 400$ m² - Side 3 area: $21 \times 25 = 525$ m² Total lateral area = $325 + 400 + 525 = 1250$ m² 5. **Calculate total surface area:** The prism has two triangular bases and three rectangular sides. $$\text{Total surface area} = 2 \times 65 + 1250 = 130 + 1250 = 1380 \text{ m}^2$$ 6. **Calculate glitter needed:** Each m² requires 60 g of glitter. $$\text{Glitter needed} = 1380 \times 60 = 82800 \text{ g}$$ 7. **Final answer:** Katie will need $$\boxed{82800}$$ grams of glitter to cover the prism.