- The best geometric shape for the model is a square pyramid.
- The approximate surface area is equal to 22,500 square feet.
What is a square pyramid?
A square pyramid can be defined as a type of pyramid that has a square base, four (4) triangular sides, five (5) vertices, and eight (8) edges.
In this context, we can logically deduce that the geometric shape which best models the object (cell phone tower) shown in the image attached above is a square pyramid.
How to calculate surface area of a square pyramid?
Mathematically, the surface area of a square pyramid is given by this formula:
A = a² + 2a√(a²/4 + h²)
Where:
- A is the surface area of a square pyramid.
- a represents the edge of the base.
Given the following parameters:
Edge of the base = 50 feet.
Height = 200 feet.
Substituting the given parameters into the formula, we have;
A = 50² + 2(50)√(50²/4 + 200²)
A = 2,500 + 100√(2500/4 + 40,000)
A = 2,500 + 100√(625 + 40,000)
A = 2,500 + 100√(40,625)
A = 2,500 + 100(201.56)
A = 2,500 + 20,156
A = 22,656 ≈ 22,500 ft².
In conclusion, the best geometric shape for the model is a square pyramid and the approximate surface area is equal to 22,500 square feet.
Read more on square pyramid here: https://brainly.com/question/23451268
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