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.
![### Understanding the Surface Area of a Pyramid
In this lesson, we will explore the surface area of a pyramid. Below is a diagram to help illustrate the components and dimensions of the pyramid.
#### Diagram Description:
- The pyramid has a square base.
- The base edges are each labeled as "16 m".
- The slant height of the pyramid faces is labeled as "15 m".
- There is an arrow indicating the length from the center of the base to the midpoint of an edge, which is denoted as "8√3 m".
#### Labels and Notations:
1. **Base Edges (16 m)**: Each side of the base of the pyramid measures 16 meters.
2. **Slant Height (15 m)**: The slant height, which is the distance from the midpoint of one of the bottom edges to the apex or top of the pyramid, measures 15 meters.
3. **Distance from Center to Midpoint of Base Edge (8√3 m)**: The distance from the center of the base to the midpoint of one of the base edges measures 8√3 meters.
#### Steps to Calculate Surface Area:
The surface area of a pyramid can be calculated using the formula:
\[ \text{Surface Area} = \text{Base Area} + \text{Lateral Surface Area} \]
1. **Base Area**:
\[
\text{Base Area} = \text{side}^2 = 16m \times 16m = 256 \text{ m}^2
\]
2. **Lateral Surface Area**:
The lateral surface area is calculated by finding the area of the four triangular faces.
\[
\text{Lateral Surface Area} = 4 \left(\frac{1}{2} \times \text{Base} \times \text{Slant Height}\right)
\]
\[
= 4 \left(\frac{1}{2} \times 16m \times 15m\right)
\]
\[
= 4 \times 120 \text{ m}^2
\]
\[
= 480 \text{ m}^2
\]
3. **Total Surface Area**:
\[
\text{Surface Area} = \text{Base Area} + \text{Lateral Surface Area}
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![## Surface Area of Pyramids
In this section, we will calculate the surface area of pyramids.
### Example Problem #4
You are given the following information:
- The height of the pyramid is \( 8 \sqrt{3} \, \text{m} \).
#### Calculate the Lateral Surface Area
Lateral surface area is denoted as:
\[ \text{Lateral: } A = \underline{\hspace{100pt}} \, \text{m}^2 \]
*Note: Please fill in your answer in the space provided.*
#### Calculate the Total Surface Area
Total surface area is denoted as:
\[ \text{Total: } A = \underline{\hspace{100pt}} \, \text{m}^2 \]
*Note: Please fill in your answer in the space provided.*
Your steps should involve identifying the slant height using the given height and then calculating the triangular faces. Add the base area if calculating the total surface area.
Use the "Back" and "Next" buttons to navigate through the questions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F00d8e2df-71d0-4b61-89d2-c93002c60192%2F4523b578-d0ce-439e-8299-1734ff050a38%2Fyw84dul_processed.jpeg&w=3840&q=75)
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