Math Problem Statement
What’s the answer
Solution
To solve the problem, we need to calculate the surface area of a triangular pyramid (also called a tetrahedron) where all faces are equilateral triangles.
Step-by-Step Solution:
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Identify the Parameters:
- Each triangle is an equilateral triangle.
- The height of each triangle is .
- The side length of each triangle is (as shown at the base).
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Formula for the Area of an Equilateral Triangle: The area of an equilateral triangle with side length is given by the formula: Here, .
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Calculate the Area of One Triangle: Substituting the side length:
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Total Surface Area: A triangular pyramid has 4 equilateral triangles. Therefore, the total surface area is:
Final Answer:
The surface area of the triangular pyramid is approximately 339.8 square feet.
Would you like more details or have any questions?
Here are some related questions you can explore:
- How is the formula for the area of an equilateral triangle derived?
- What is the volume of this triangular pyramid?
- How do you calculate the height of an equilateral triangle if the side length is known?
- What if the base was not an equilateral triangle, how would the surface area change?
- How does the surface area of this pyramid compare to a square pyramid with the same base length?
Tip: Always remember that in an equilateral triangle, the relationship between side length and height is useful for multiple geometric applications.
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Math Problem Analysis
Mathematical Concepts
Geometry
Surface Area
Equilateral Triangle
Formulas
Area of an equilateral triangle: A = (s^2 * sqrt(3)) / 4
Surface area of a triangular pyramid: A_total = 4 * A
Theorems
Pythagorean theorem (used to calculate triangle properties)
Equilateral triangle properties
Suitable Grade Level
Grades 9-10
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