What is the formula to calculate the surface area of a square-based pyramid?

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The surface area $$ \text{SA} $$ of a square-based pyramid can be calculated using the following formula:

$$
\text{SA} = a^2 + 2a \cdot l
$$

**Where:**
- $$ a $$ is the length of one side of the square base.
- $$ l $$ is the slant height of the pyramid (the distance from the base edge to the apex along the face).

**Breakdown of the Formula:**

1. **Base Area ($$ a^2 $$):**
   - Since the base is a square, its area is side length squared.

2. **Lateral (Triangular) Faces Area ($$ 2a \cdot l $$):**
   - There are four triangular faces in a square-based pyramid.
   - Each triangular face has an area of $$ \frac{1}{2} \times a \times l $$.
   - So, the combined area of the four triangles is $$ 4 \times \frac{1}{2} \times a \times l = 2a \cdot l $$.

**Complete Formula:**
$$
\text{SA} = \text{Base Area} + \text{Lateral Faces Area} = a^2 + 2a \cdot l
$$

**Example:**
If a square-based pyramid has a base side length of 5 units and a slant height of 7 units, its surface area would be:

$$
\text{SA} = 5^2 + 2 \times 5 \times 7 = 25 + 70 = 95 \text{ square units}
$$
The surface area of a square-based pyramid is calculated using the formula: $$ \text{SA} = a^2 + 2a \cdot l $$ Where: - $$ a $$ is the length of one side of the square base. - $$ l $$ is the slant height of the pyramid. **Example:** For a pyramid with a base side of 5 units and a slant height of 7 units, the surface area is: $$ \text{SA} = 5^2 + 2 \times 5 \times 7 = 25 + 70 = 95 \text{ square units} $$

What is the formula to calculate the surface area of a square-based pyramid?

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