Question
Question 3) A triangular prism has a base area of 26 square units and a volume of 208 cubic units. What is the height of the prism? 6 7 8 9
Ask by Pena Harrington. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The height of the prism is 8 units.
Solution
To find the height of the triangular prism, we can use the formula for the volume of a triangular prism:
\[ \text{Volume} = \text{Base Area} \times \text{Height} \]
Given:
- Base Area = 26 square units
- Volume = 208 cubic units
We can rearrange the formula to solve for the height:
\[ \text{Height} = \frac{\text{Volume}}{\text{Base Area}} \]
Substitute the given values:
\[ \text{Height} = \frac{208}{26} \]
Now, we can calculate the height of the prism.
Calculate the value by following steps:
- step0: Calculate:
\(\frac{208}{26}\)
- step1: Reduce the numbers:
\(\frac{8}{1}\)
- step2: Calculate:
\(8\)
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Bonus Knowledge
To find the height of a triangular prism, you can use the formula for volume, which is Volume = Base Area × Height. You've got the base area (26 square units) and the volume (208 cubic units). Rearanging the formula gives us Height = Volume / Base Area. So, plugging in the numbers, Height = 208 / 26, which gives you a height of 8 units. And voilà, you've found that the height of the prism is 8 units—a simple calculation leading to a solid number! 🎉 Now you can impress your friends with both your math skills and your knowledge of prisms!