What is the surface area of Sally’s Pyraminx?

Question

Write your answer in decimal form. Round to the nearest thousandth.
A three-sided pyramid has sides measuring 4 and the height of the pyramid is 3.646 in.

Answer 1

To find the surface area of the Pyraminx, we first need to calculate the lateral area of the pyramid and then add the area of the base.

1. Lateral Area:
Lateral Area = (Perimeter of base) * (slant height) / 2

Perimeter of base = 4 + 4 + 4 = 12
Slant height = √(4^2 + 3.646^2) = √(16 + 13.289116) = √29.289116 = 5.412486

Lateral Area = 12 * 5.412486 / 2 = 32.474916 in^2

2. Area of base:
Area of base = (base side)^2 = 4^2 = 16 in^2

3. Total Surface Area:
Total Surface Area = Lateral Area + 3 * Area of base = 32.474916 + 3 * 16 = 32.474916 + 48 = 80.474916 in^2

Therefore, the surface area of Sally's Pyraminx is approximately 80.475 square inches when rounded to the nearest thousandth.

Answer 2

the correct answer is 29.168

Answer 3

I apologize for the mistake in my calculation. Let's correct that:

1. Lateral Area:
Lateral Area = (Perimeter of base) * (slant height) / 2

Perimeter of base = 4 + 4 + 4 = 12
Slant height = √(4^2 + 3.646^2) = √(16 + 13.289116) = √29.289116 = 5.412486

Lateral Area = 12 * 5.412486 / 2 = 32.474916 in^2

2. Area of base:
Area of base = (base side)^2 = 4^2 = 16 in^2

3. Total Surface Area:
Total Surface Area = Lateral Area + Area of base = 32.474916 + 16 = 48.474916 in^2

Therefore, the correct surface area of Sally's Pyraminx is approximately 48.475 square inches when rounded to the nearest thousandth. Thank you for pointing out the mistake.