The length of a side of the base of a regular square pyramid is 5 inches. And the pyramid’s slant hight is 18 inches. Find the surface area of the pyramid 

The surface area of a regular square pyramid consists of the area of the square base and the area of the four triangular faces (lateral surface area). 

### Step 1: Find the area of the base
Since the base is a square, the area of the base \( A_{\text{base}} \) is:
\[
A_{\text{base}} = \text{side length}^2 = 5^2 = 25 \, \text{square inches}
\]

### Step 2: Find the area of one triangular face
The area of a triangular face is given by:
\[
A_{\text{triangle}} = \frac{1}{2} \times \text{base of triangle} \times \text{slant height}
\]
Here, the base of each triangular face is the side length of the square, which is 5 inches, and the slant height is 18 inches. Therefore:
\[
A_{\text{triangle}} = \frac{1}{2} \times 5 \times 18 = \frac{1}{2} \times 90 = 45 \, \text{square inches}
\]

### Step 3: Find the lateral surface area
Since the pyramid has 4 triangular faces, the total lateral surface area is:
\[
A_{\text{lateral}} = 4 \times A_{\text{triangle}} = 4 \times 45 = 180 \, \text{square inches}
\]

### Step 4: Calculate the total surface area
The total surface area \( A_{\text{total}} \) of the pyramid is the sum of the area of the base and the lateral surface area:
\[
A_{\text{total}} = A_{\text{base}} + A_{\text{lateral}} = 25 + 180 = 205 \, \text{square inches}
\]

Thus, the surface area of the pyramid is **205 square inches**.

Would you like more details or have any questions?

Here are some related questions you might find helpful:
1. How do you calculate the volume of a pyramid with the same dimensions?
2. What is the formula for the surface area of a pyramid with different base shapes?
3. How does the slant height affect the surface area of a pyramid?
4. What would the surface area be if the base was a rectangle instead of a square?
5. How does changing the height of the pyramid (but not the slant height) affect the surface area?

**Tip:** Always double-check whether you're asked for surface area or volume, as these two measurements are often confused.

The length of a side of the base of a regular square pyramid is 5 inches. And the pyramid’s slant height is 18 inches. Find the surface area of the pyramid.

Find out how to calculate the surface area of a regular square pyramid with a 5-inch base and an 18-inch slant height. This problem involves geometry concepts such as surface area, triangular faces, and lateral surface area. Step-by-step solution provided, suitable for Grades 8-10.

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