A regular pentagon is such that its vertices lies on the circumference of a circle of radius 4.5cm.Find the length of a side of the pentagon to the nearest mm
To find the length of a side of the pentagon, we can start by calculating the circumference of the circle with a radius of 4.5 cm.
The formula for the circumference of a circle is: circumference = 2πr, where r is the radius of the circle.
Given that the radius is 4.5 cm, we can substitute this value into the formula:
circumference = 2 * π * 4.5 cm
To find the length of a side of the pentagon, we need to divide the circumference of the circle by 5 since there are 5 sides in a regular pentagon.
Side length = circumference / 5
Side length = (2 * π * 4.5 cm) / 5
To simplify the calculation, we can approximate the value of π to 3.14:
Side length ≈ (2 * 3.14 * 4.5 cm) / 5
Side length ≈ (28.26 cm) / 5
Side length ≈ 5.65 cm
Therefore, the length of a side of the pentagon is 5.65 cm to the nearest mm.
The pentagon consists of 5 isosceles triangles, with vertex angle 360/5 = 72°, and two sides of length 4.5 cm. So the base of the triangle (the side of the pentagon) is
s = 2*4.5sin36° cm
To find the length of a side of a regular pentagon, we can use the formula:
s = 2r sin(π/5)
Where:
s is the length of a side,
r is the radius of the circle,
π is a mathematical constant approximately equal to 3.14159.
Given that the radius (r) is 4.5 cm, we can substitute this value into the formula:
s = 2(4.5 cm) sin(π/5)
Using the radius, the formula becomes:
s = 9 cm sin(π/5)
Now, let's calculate the value of sin(π/5):
sin(π/5) ≈ 0.5878
Substituting this value back into the formula:
s = 9 cm × 0.5878
s ≈ 5.2902 cm
Finally, rounding to the nearest millimeter, the length of a side of the pentagon is approximately 5.3 cm.