Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![### Volume Calculation of a Triangular Prism
**Problem Statement:**
Here is a triangular prism with the following dimensions:
- Side of the triangle: 6 inches
- Side of the triangle: 8 inches
- Hypotenuse of the triangle (Base 1): 10 inches
- Height of the prism: 12 inches
**Question:**
What is the volume of the prism, in cubic inches?
**Diagram Explanation:**
The diagram showcases a triangular prism with given dimensions. The front face of the prism is labeled as a right triangle with sides measuring 6 inches and 8 inches. The hypotenuse (the longest side) is 10 inches. The prism extends to a height (or length) of 12 inches.
**Solution:**
1. **Determine the Area of the Triangular Base:**
The base of the triangular face is a right triangle. The area of a right triangle is calculated using the formula:
\[
\text{Area} = \frac{1}{2} \times \text{base 1} \times \text{base 2}
\]
Substituting the given values:
\[
\text{Area} = \frac{1}{2} \times 6 \times 8 = 24 \text{ square inches}
\]
2. **Calculate the Volume of the Prism:**
The volume of a prism is found by multiplying the area of the base by the height (length) of the prism:
\[
\text{Volume} = \text{Base Area} \times \text{Height}
\]
Using the given height of 12 inches:
\[
\text{Volume} = 24 \times 12 = 288 \text{ cubic inches}
\]
**Answer:**
The volume of the prism is 288 cubic inches.
This explanation and solution should provide a clear understanding of how to approach and solve problems involving the volume of a triangular prism.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb1bd361c-1b6a-482c-8d82-604310d05b6c%2F69689104-bd26-45f4-94d3-860ba2761586%2Fu3w8h74_processed.jpeg&w=3840&q=75)
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