What is the surface area of Sally’s Pyraminx?

Question

Write your answer in decimal form. Round to the nearest thousandth.
A pyraminx is a triangula piramid, Its base and height are 4 in.
Use a slant height of 3.646 in. for this question

Answer 1

The surface area of Sally's Pyraminx can be calculated using the formula:

Surface area = base area + (1/2 * perimeter * slant height)

First, calculate the base area of the pyramid:
Base area = 1/2 * base * height
Base area = 1/2 * 4 * 4
Base area = 8 square inches

Next, calculate the perimeter of the base:
Perimeter = 3 * base
Perimeter = 3 * 4
Perimeter = 12 inches

Now, plug in the base area, perimeter, and slant height into the formula:
Surface area = 8 + (1/2 * 12 * 3.646)
Surface area = 8 + (1/2 * 12 * 3.646)
Surface area = 8 + (6 * 3.646)
Surface area = 8 + 21.876
Surface area = 29.876

Therefore, the surface area of Sally's Pyraminx is approximately 29.876 square inches.