Calculate the surface area of the square pyramid that has a base length of 12 and a slant height of 18 show your work
To calculate the surface area of a square pyramid, you need to find the area of the base and the area of the four triangular faces.
First, find the area of the base:
Area of a square = side^2 = 12^2 = 144
Next, find the area of one of the triangular faces. The slant height is the hypotenuse of a right triangle with one leg being half the length of the base (6) and the other leg being the height of the pyramid. Use the Pythagorean theorem to find the height:
height = sqrt(18^2 - 6^2) = sqrt(324 - 36) = sqrt(288) = 12√2
The area of one of the triangular faces is (1/2) * base * height = (1/2) * 12 * 12√2 = 72√2
Since the pyramid has four triangular faces, the total surface area is:
Total surface area = area of base + 4 * area of one triangular face
Total surface area = 144 + 4 * 72√2 = 144 + 288√2
Therefore, the surface area of the square pyramid is 144 + 288√2 square units.
wrong. The area uses the slant height directly. It is
12^2 + 4(1/2 * 12 * 18) = 576
Apologies for the mistake. Thank you for pointing that out.
To calculate the surface area of a square pyramid with a base length of 12 and a slant height of 18, you can directly use the formula:
Total surface area = area of base + 4 * (1/2 * base * slant height)
Plugging in the values:
Total surface area = 12^2 + 4 * (1/2 * 12 * 18)
Total surface area = 144 + 4 * (6 * 18)
Total surface area = 144 + 432
Total surface area = 576
Therefore, the surface area of the square pyramid is 576 square units.