what is the surface area of a square pyramid if the slant height is 15.2 m and the base is 15.2 m?

please explain it to me. this is not homework, it is a practice question and I do not understand how to solve it. Someone PLEASE help!

as illustrated and explained here:

http://math.about.com/od/formulas/ss/surfaceareavol_5.htm

the area is just the square area of the base plus the areas of the four triangles forming the sides. And, as we all know, the area of a triangle is 1/2 base * height (the slant height of the pyramid). So,

A = b^2 + 2bs = 15.2^2 + 2(15.2)(15.2) = ?

To find the surface area of a square pyramid, you need to calculate the areas of the square base and the triangular faces. Let's go step by step to solve this problem.

1. Start with the formula for the surface area of a square pyramid:
Surface Area = Base Area + 4 * Triangle Area

2. Find the base area:
For a square pyramid, the base area is simply the area of the square base. Since the base is a square, you can use the formula: Base Area = side length * side length.

In this case, the side length of the base is given as 15.2 m, so the base area would be:
Base Area = 15.2 m * 15.2 m = 231.04 m²

3. Find the triangle area:
Each triangular face of the pyramid is an isosceles triangle. We need the height of the triangle to calculate the area. The height can be found using the Pythagorean theorem.

The slant height of the pyramid is given as 15.2 m. To find the height of the triangle, follow these steps:
- Use the formula of a right triangle: (base/2)² + height² = slant height².
- Plug in the values: (15.2/2)² + height² = 15.2².
- Simplify and solve for height: (7.6)² + height² = 231.04. Subtracting (7.6)² gives height² = 231.04 - (7.6)². Calculate height and round the result to the appropriate number of decimal places.

4. Calculate the triangle area:
Now that we have the height of the triangle, we can use the formula for the area of an isosceles triangle:
Triangle Area = (base * height) / 2

In this case, the base length is 15.2 m and the height was calculated in the previous step. Plug in the values to find the triangle area.

5. Calculate the surface area:
With the base area (step 2) and the triangle area (step 4), you can now find the surface area using the formula from step 1:
Surface Area = Base Area + 4 * Triangle Area

Plug in the respective values and calculate the surface area.

By following these steps, you'll be able to solve for the surface area of the square pyramid.