The surface area of Sally's Pyraminx can be calculated using the formula for the surface area of a triangular pyramid, which is given by:
Surface Area = base area + (1/2) * perimeter of base * slant height
First, we need to calculate the base area and perimeter of the base of the equilateral triangle:
Base Area = (sqrt(3) / 4) * side^2
Base Area = (sqrt(3) / 4) * 4^2
Base Area = (sqrt(3) / 4) * 16
Base Area = 4 * sqrt(3)
Perimeter of the Base = 3 * side
Perimeter of the Base = 3 * 4
Perimeter of the Base = 12
Next, we calculate the slant height using the Pythagorean theorem:
Slant Height = sqrt(height^2 + (side/2)^2)
Slant Height = sqrt(3.646^2 + 2^2)
Slant Height = sqrt(13.291 - 4)
Slant Height = sqrt(9.291)
Slant Height = 3.047
Now, we can plug in the values into the surface area formula:
Surface Area = 4 * sqrt(3) + (1/2) * 12 * 3.047
Surface Area = 4 * sqrt(3) + 18.282
Surface Area ≈ 4 * 1.732 + 18.282
Surface Area ≈ 6.928 + 18.282
Surface Area ≈ 25.21
Therefore, the surface area of Sally's Pyraminx is approximately 25.21 square inches.
PLEASE answer correctly and use the details i give you to answer the question.
Two front faces of a triangular pyramid are shown. Each face shows three levels of triangle shapes: 1 at the top, 3 in the middle row, and 5 along the bottom row. The orientation of the triangles alternates from upright to inverted on the bottom two rows. The sides of the triangular pyramid are equilateral and measure 4 inches. The vertical height measures 3.646 inches.
What is the surface area of Sally’s Pyraminx? Write your answer in decimal form. Round to the nearest thousandth.
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