Question

alculate 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 of the pyramid is a square, the area of the base can be calculated by squaring the base length:
Base area = 12^2 = 144

2. Area of each triangular face:
The slant height is perpendicular to the base of the pyramid, so the height of each triangular face can be found using the Pythagorean theorem:
h = √(s^2 - (1/2 * base)^2)
h = √(18^2 - (1/2 * 12)^2)
h = √(324 - 36)
h = √288
h ≈ 16.97

Since the height is not a whole number, we will use the approximate value for calculations.

Now, calculate the area of one triangular face using the base length and height:
Triangular face area = 1/2 * base * height
Triangular face area = 1/2 * 12 * 16.97
Triangular face area ≈ 101.82

3. Total surface area:
Since there are four triangular faces, the total surface area of the pyramid is the sum of the base area and the four triangular face areas:
Total surface area = base area + 4 * triangular face area
Total surface area = 144 + 4 * 101.82
Total surface area = 144 + 407.28
Total surface area = 551.28

Therefore, the surface area of the square pyramid is approximately 551.28 square units.