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The problem describes a square pyramid \( T.ABCD \), where \( AB = 18 \, \text{cm} \) (the side length of the square base) and the slant height (the height of the triangular face) is \( 15 \, \text{cm} \). We are asked to find the total surface area of the pyramid.

To solve this, we need to calculate two areas:
1. The area of the square base.
2. The area of the four triangular faces.

### Step 1: Calculate the area of the square base
The area of the square base is given by:
\[
\text{Area of base} = AB^2 = 18^2 = 324 \, \text{cm}^2
\]

### Step 2: Calculate the area of the triangular faces
Each triangular face is an isosceles triangle with a base of \( AB = 18 \, \text{cm} \) and a slant height of \( 15 \, \text{cm} \). The area of one triangular face is:
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 18 \times 15 = 135 \, \text{cm}^2
\]
Since there are 4 triangular faces, the total area of the triangular faces is:
\[
\text{Total area of triangles} = 4 \times 135 = 540 \, \text{cm}^2
\]

### Step 3: Calculate the total surface area
The total surface area of the pyramid is the sum of the area of the base and the area of the triangular faces:
\[
\text{Total surface area} = 324 + 540 = 864 \, \text{cm}^2
\]

Thus, the total surface area of the pyramid is **864 cm²**.

Would you like further clarification or details on any part of the process?

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Here are some related questions you can explore:
1. How would the total surface area change if the side length of the base was doubled?
2. What is the formula for the volume of a square pyramid?
3. How can you derive the slant height if only the height of the pyramid is given?
4. What is the difference between the slant height and the height of the pyramid?
5. How would you calculate the surface area if the pyramid had a rectangular base?

**Tip:** Remember, the slant height is not the same as the vertical height of the pyramid; it's the height of the triangular face!

T.ABCD adalah limas persegi dengan AB = 18 cm. Jika tinggi sisi tegaknya 15 cm, maka luas seluruh permukaan limas adalah ....

Learn how to calculate the total surface area of a square pyramid with a side length of 18 cm and slant height of 15 cm. This guide provides a detailed breakdown of calculating the base area and the triangular face areas, culminating in the total surface area calculation.

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