Calculate the surface area of the square pyramid that has a base length of 12 and a slant height of 18. Show your work..

Answer 1

To calculate the surface area of a square pyramid, we need to find the area of the base and the area of the four triangular faces.

1. Area of the base:
Since the base is a square, the area is calculated as length * width.
Area of the base = 12 * 12 = 144 square units

2. Area of each triangular face:
The area of a triangle can be calculated using the formula: 0.5 * base * height.
Since the base of the triangular face is the same as the side length of the square base (12), we need to find the height. The height can be found using the Pythagorean theorem:
height^2 = (slant height)^2 - (side length / 2)^2
height^2 = 18^2 - 6^2
height^2 = 324 - 36
height^2 = 288
height = sqrt(288) = 12√2

Now we can calculate the area of each triangular face:
Area of each triangular face = 0.5 * 12 * 12√2 = 72√2 square units

3. Total surface area:
Total surface area = Area of base + 4 * Area of triangular face
Total surface area = 144 + 4 * 72√2
Total surface area = 144 + 288√2
Total surface area ≈ 376.48 square units

Therefore, the surface area of the square pyramid is approximately 376.48 square units.

Answer 2

make it look like a 7th grader wrote it

Answer 3

To find the surface area of a square pyramid, we first need to find the area of the square base. The base has a length of 12, so the area is 12 x 12 = 144 square units.

Next, we need to find the area of each of the four triangular faces. Each face has a base of 12 and a height of 12√2. We can calculate this as 0.5 x 12 x 12√2 = 72√2 square units for each face.

Now, we add the area of the base to the total area of the four triangular faces to get the total surface area:
Total surface area = 144 + 4 x 72√2
Total surface area = 144 + 288√2
Total surface area is approximately equal to 376.48 square units.

So, the surface area of the square pyramid is about 376.48 square units.