Question

1. mp problem solving 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.

Explanation:

Step1: Recall the area formula for a triangle

The area of a triangle is given by $A = \frac{1}{2} \times base \times height$. Here, the base of each triangular face is the side length of the square base (116 feet) and the height of each triangular face is 91.7 feet.

Step2: Calculate the area of one triangular face

Substitute the values into the formula: $A_{one} = \frac{1}{2} \times 116 \times 91.7$. First, calculate $\frac{1}{2} \times 116 = 58$. Then, $58 \times 91.7 = 5318.6$ square feet.

Step3: Calculate the area of four triangular faces

Since there are four identical triangular faces, multiply the area of one face by 4: $A_{total} = 4 \times 5318.6 = 21274.4$ square feet.

Answer:

The surface area of the four triangular faces is 21274.4 square feet.