Answer:
Perimeter ≈ 28.95mm
Explanation:
The perimeter of the tile can be found by adding up the lengths of all its sides.
First, let's find the perimeter of the semi-circle. The curved side of the semi-circle is given as 13.3mm, which is equal to half the circumference of the semi-circle. We can use the formula for the circumference of a circle to find the full circumference of the semi-circle:
C = 2πr
where C is the circumference, π is a constant equal to approximately 3.14, and r is the radius of the circle. In this case, the curved side is equal to half the circumference, so we can solve for the radius:
13.3mm = (1/2)C
C = 26.6mm
C = 2πr
26.6mm = 2πr
r = 26.6mm / (2π) ≈ 4.23mm
Now that we have the radius, we can find the length of the straight edge of the semi-circle by using the Pythagorean theorem. The diameter of the semi-circle is equal to the length of one side of the square, which is 9.4mm. The diameter is also equal to the sum of the straight edge of the semi-circle (which we are trying to find) and twice the radius. Therefore:
(Length of straight edge)^2 + (2 x radius)^2 = (Diameter)^2
(Length of straight edge)^2 + (2 x 4.23mm)^2 = (9.4mm)^2
(Length of straight edge)^2 = (9.4mm)^2 - (2 x 4.23mm)^2
(Length of straight edge) ≈ 7.30mm
Finally, we can find the perimeter of the tile by adding up the lengths of all its sides:
Perimeter = (Length of square side) + (Length of straight edge of semi-circle) + (Half the circumference of the semi-circle)
Perimeter = 9.4mm + 7.30mm + 13.3mm/2
Perimeter ≈ 28.95mm
Therefore, the perimeter of the whole tile is approximately 28.95mm.