calculate the surface area of the square pyramid that base a base length of 12 and a slant height of 18 show ur work
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Given:
Base length (s) = 12
Slant height (l) = 18
1. Calculate the area of the base:
Base area = s^2 = 12^2 = 144 sq units
2. Calculate the area of the four triangular faces:
Each triangular face area = (1/2) * s * l = (1/2) * 12 * 18 = 108 sq units
Total area of all four faces = 4 * 108 = 432 sq units
3. Add the base area and the total area of the four faces to get the total surface area:
Total surface area = Base area + Total face area = 144 + 432 = 576 sq units
Therefore, the surface area of the square pyramid with a base length of 12 and a slant height of 18 is 576 square units.
To calculate the surface area of a square pyramid, we need to find the total area of the base and the area of the four triangular faces.
The base of the pyramid is a square with a side length of 12. The area of the base is 12^2 = 144 square units.
The slant height of the pyramid is 18. This slant height forms the hypotenuse of a right triangle, with one leg being half the length of the base side (6) and the height of the pyramid (h) as the other leg.
We can use the Pythagorean theorem to find the height:
h^2 = 18^2 - 6^2
h^2 = 324 - 36
h^2 = 288
h = sqrt(288)
h = 16.97 (rounded to nearest hundredth)
Now, we can calculate the area of each triangular face:
A = (1/2) * base * height
A = (1/2) * 12 * 16.97
A = 101.82 square units
There are four triangular faces, so the total area for all faces is 4 * 101.82 = 407.28 square units
Finally, we add the area of the base and the triangular faces to get the total surface area of the square pyramid:
Total surface area = 144 + 407.28 = 551.28 square units
Therefore, the surface area of the square pyramid with a base length of 12 and a slant height of 18 is 551.28 square units.