The great pyramid of Giza was built around 2560 BC. It was originally 481ft high with a square base measuring 751 ft on each side. It's slant height was 611 ft. Find the lateral surface area of the great pyramid, round your answer to the four-significant digits? How do I start this thing?
There are four triangles, each with a area of 1/2 bh= 1/2 (611*751).
To find the lateral surface area of the great pyramid of Giza, we need to calculate the sum of the areas of the four triangular faces.
1. Begin by calculating the base area of one of the triangular faces:
- The base side length is 751 ft, so the base area is (751 ft)².
2. Determine the height of the triangular face:
- The height of the triangular face can be found using the Pythagorean theorem, with the base side length and the slant height.
- We can use the formula: height = √(slant height² - base side length²/4).
- Plugging in the values, we get: height = √((611 ft)² - (751 ft)²/4).
3. Calculate the area of the triangular face:
- Use the formula for the area of a triangle: area = 0.5 * base * height.
- The base for each triangular face is the base side length (751 ft), and the height was calculated in step 2.
4. Multiply the area of one triangular face by 4 to get the lateral surface area of the pyramid.
Now let's calculate the answer:
- Base area = (751 ft)².
- Height = √((611 ft)² - (751 ft)²/4).
- Area of one triangular face = 0.5 * (751 ft) * height.
- Lateral surface area = 4 * area of one triangular face.
Plug in the above values into a calculator or spreadsheet and round the answer to four significant digits for the final result.