Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
![### Pentagonal Pyramid Surface Area Calculation
In this figure, we have a pentagonal pyramid with the following measurements:
- **Slant height**: 10.5 inches
- **Base area (B)**: 247.75 square inches
- **Base edge length**: 12 inches
We need to calculate the lateral area (LA) and surface area (SA) of the pyramid.
#### Lateral Area (LA) Calculation:
The lateral area of a pyramid can be calculated using the formula:
\[ LA = \frac{1}{2} \times P \times l \]
where:
- \( P \) is the perimeter of the base
- \( l \) is the slant height of the pyramid
#### Surface Area (SA) Calculation:
The surface area of a pyramid is given by:
\[ SA = LA + B \]
where:
- \( B \) is the area of the base
**Given Data:**
- Base edge length = 12 inches
- Number of base edges = 5 (since it's a pentagon)
- Slant height (\( l \)) = 10.5 inches
- Base area (\( B \)) = 247.75 square inches
**Step-by-step Calculation:**
1. **Calculate the perimeter \( P \) of the base:**
\[ P = 5 \times 12 = 60 \text{ inches} \]
2. **Calculate the lateral area \( LA \):**
\[ LA = \frac{1}{2} \times 60 \times 10.5 = 315 \text{ square inches} \]
3. **Calculate the surface area \( SA \):**
\[ SA = LA + B \]
\[ SA = 315 + 247.75 = 562.75 \text{ square inches} \]
Therefore:
\[ LA = 315 \text{ square inches} \]
\[ SA = 562.75 \text{ square inches} \]
This concludes our calculation for the lateral area and surface area of the given pentagonal pyramid.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2a5f7bb8-38e7-4a5a-bfc7-c8f4b1290a9a%2Ffc313216-9795-4ffb-9d92-f2d9d2eea2e2%2Fky1fo9_processed.jpeg&w=3840&q=75)
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