A square-based pyramid has base side lengths of 38 feet and a slant height of 24 feet. What is the surface area of its sides, not including the base?
a. 1824 f
b. 3648 ft²
c. 912 ft² d. 456 ft²
The surface area of a square-based pyramid can be calculated by finding the sum of the areas of all its triangular faces. In this case, we have 4 triangular faces.
The area of a triangle can be found using the formula A = 0.5 * base * height.
The base of each triangle is 38 feet (the side length of the square base), and the height can be found using the Pythagorean theorem. The height of the triangle is the slant height of the pyramid, which is 24 feet. The height (h) can be found by using the formula h = √(slant height² - base length/2)².
h = √(24² - (38/2)²)
h = √(576 - 19²)
h = √(576 - 361)
h = √215
h ≈ 14.66 feet
Now we can calculate the area of each triangle:
A = 0.5 * base * height
A = 0.5 * 38 * 14.66
A ≈ 277.67 ft²
Since we have 4 triangles, the total surface area of the sides (not including the base) is 4 times the area of one triangle:
Total surface area = 4 * 277.67
Total surface area ≈ 1110.67 ft²
Therefore, the correct answer is d. 456 ft² is not the correct surface area of the sides, not including the base, of the square-based pyramid.