Question
If all the triangles are equilateral, what is the surface area of the pyramid, in square inches? 10.39 in 12 in
Answers
GPT 3.5
The surface area of an equilateral triangle is given by the formula A = (√3/4) * s^2, where s is the length of a side of the triangle.
Since all the triangles in the pyramid are equilateral and have a side length of 12 inches, the surface area of each triangle is:
A = (√3/4) * 12^2
A = (√3/4) * 144
A = (√3 * 144) / 4
A = (12√3) / 4
A = 3√3
Since there are four triangles in the pyramid, the total surface area of the pyramid is:
4 * 3√3
= 12√3
Approximately, the surface area is:
12√3 ≈ 20.78 square inches
Therefore, the surface area of the pyramid is approximately 20.78 square inches.
Since all the triangles in the pyramid are equilateral and have a side length of 12 inches, the surface area of each triangle is:
A = (√3/4) * 12^2
A = (√3/4) * 144
A = (√3 * 144) / 4
A = (12√3) / 4
A = 3√3
Since there are four triangles in the pyramid, the total surface area of the pyramid is:
4 * 3√3
= 12√3
Approximately, the surface area is:
12√3 ≈ 20.78 square inches
Therefore, the surface area of the pyramid is approximately 20.78 square inches.