Question

The entrance to the Louvre Museum in Paris, France, is a square pyramid. The side length of the base is 116 feet, and the height of one of the triangular faces is 91.7 feet. Find the surface area of the four triangular faces of the entrance to the Louvre Museum

Answer 1

The surface area of the four triangular faces of the Louvre Museum entrance pyramid is 21293.6 square feet.

Step-by-step explanation:

To find the surface area of the four triangular faces of the pyramid, we need to calculate the area of one triangular face and then multiply it by 4. The area of a triangle can be calculated using the formula A = (1/2)bh, where A is the area, b is the base length, and h is the height. In this case, the base length is 116 feet and the height is 91.7 feet.

Plugging the values into the formula, we get A = (1/2)(116)(91.7) = 5323.4 square feet for one triangular face. To find the surface area of all four triangular faces, we multiply this value by 4: 5323.4 * 4 = 21293.6 square feet.

Answer 2

The length of the base of any of the triangular faces is 91.7 ft, and the height of that face is 91.7 ft, measured from this base to the pinnacle (vertex).

The area of this one face is thus A = bh/2, which comes out to
A=(116 ft)(91.7 ft)/2. Multiply this result by four:

Total A = 4(116)(91.7)/2) = 21274 sq ft (where I have rounded off the answer to the nearest unit).