The Great Pyramid of Giza has a square base with side length of 755 ft. and an original height of 481 ft. Determine its original surface area to the nearest square foot.
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To determine the original surface area of the Great Pyramid of Giza, we need to calculate the sum of the areas of all four triangular faces and the square base.
1. Begin by calculating the area of the triangular faces:
- Each triangular face is an isosceles triangle, with two equal sides and an included angle of 90 degrees at the base. Since the base of the pyramid is a square with a side length of 755 ft, the two equal sides of the triangular faces will also be 755 ft.
- To find the area of an isosceles triangle, we can use the formula (base * height) / 2. The height can be determined using the Pythagorean theorem.
- The height (h) of the triangular face can be calculated as √(755^2 - (755/2)^2), since it forms a right triangle with one side being half of the base (755/2).
- So, h = √(566025 - 284402.5) ≈ √281622.5 ≈ 530.844 ft.
- The area of each triangular face can be calculated as (755 * 530.844) / 2 = 200859.67 square feet.
2. Next, calculate the area of the square base:
- The area of a square is given by multiplying the lengths of two adjacent sides, in this case, 755 ft * 755 ft = 570025 square feet.
3. Finally, calculate the total surface area of the pyramid by summing the areas of the four triangular faces and the square base:
- Total surface area = 4 * (area of triangular face) + (area of square base)
- Total surface area ≈ 4 * 200859.67 + 570025
- Total surface area ≈ 803438.68 + 570025
- Total surface area ≈ 1,373,463 square feet (rounded to the nearest square foot).
Therefore, the original surface area of the Great Pyramid of Giza, to the nearest square foot, is estimated to be 1,373,463 square feet.