The Transamerica Pyramid in San Francisco is shaped like a square pyramid. It has a slant height of 856.1 feet and each side of its base is 145 feet. Find the lateral area of the building.
each face is a triangle of height s and base b, so
lateral area = 2bs = 2*145*856.1
To find the lateral area of the Transamerica Pyramid, we need to calculate the total area of the four triangular faces.
First, let's calculate the base area of each triangular face. Each triangular face is an isosceles triangle with two sides of length 145 feet and a base of length equal to the slant height, which is 856.1 feet.
Using the formula for the area of an isosceles triangle:
Area = (base * height) / 2,
we can find the height of each triangular face.
Using the Pythagorean theorem:
145^2 = (856.1)^2 + (height)^2,
we can solve for the height:
height = √(145^2 - 856.1^2).
Calculating this expression:
height = √(21025 - 732669.21) = √(-711644.21) ≈ 844.36 feet.
Now that we have the height, we can calculate the area of each triangular face:
Area = (base * height) / 2 = (145 * 844.36) / 2 ≈ 61534.2 square feet.
Since there are four triangular faces, we multiply the area of one triangular face by 4:
Total lateral area = 61534.2 * 4 = 246136.8 square feet.
Therefore, the lateral area of the Transamerica Pyramid is approximately 246136.8 square feet.
To find the lateral area of a square pyramid, you need to calculate the sum of the areas of the four triangular faces.
The formula for the lateral area of a square pyramid is:
Lateral Area = base perimeter × slant height ÷ 2
First, calculate the base perimeter of the pyramid by multiplying the length of one side by the number of sides (since a square has four sides):
Base perimeter = 4 × 145 feet = 580 feet
Next, substitute the values into the formula:
Lateral Area = 580 feet × 856.1 feet ÷ 2
Now, calculate the lateral area:
Lateral Area ≈ 248,878 square feet
Therefore, the lateral area of the Transamerica Pyramid in San Francisco is approximately 248,878 square feet.