The Great Pyramid of Giza was built around the year 2560 BC. It was originally 481 ft high with a square base measuring 751 ft on each side. Its slant height was 611ft. Find the lateral surface area of the Great Pyramid. Round your answer to four significant digits.
a. 90,430,000 ft 2 b.1,481,700 ft 2 c.917,700ft2 d. 722,500 ft 2
To find the lateral surface area of the Great Pyramid, we need to calculate the area of each triangular face and then add them together.
First, let's calculate the area of one triangular face. We can do this using the formula for the area of a triangle:
Area = 1/2 * base * height
In this case, the base of the triangle is the side length of the square base of the pyramid, which is 751 ft, and the height is the slant height of the pyramid, which is 611 ft. Plugging these values into the formula, we get:
Area = 1/2 * 751 ft * 611 ft
Now, multiply the base and the height:
Area = 375.5 ft * 611 ft
Next, we need to determine the total number of triangular faces on the pyramid. A pyramid has four faces, so the lateral surface area is the total area of the triangular faces. Since all the triangular faces are identical, we can multiply the area of one triangular face by 4:
Lateral Surface Area = 4 * Area
Lateral Surface Area = 4 * (375.5 ft * 611 ft)
Now, multiply the area by 4:
Lateral Surface Area = 1502 ft * 611 ft
Finally, we can calculate the lateral surface area by multiplying these two values:
Lateral Surface Area ≈ 917,698 ft²
Therefore, the correct answer is option c. 917,700 ft²