Answer to Question #121000 in Geometry for Tina

Question

2.1 If a regular decagonal field is fenced with a 2 250 cm wire mesh, show by calculations
the length of each side in metres.
2.2 If the sum of the interior angles of a regular polygon is 2 160˚, how many sides does it
have? Show all the steps of your calculation.
2.3 Find the total surface area of a cylinder whose radius is 14cm and the height is 20cm, if
it is closed on both sides. Show your calculations.

Answer 1

Solution:

2.1 The perimeter of the decagonal field is 2250 cm.

Then the length of each side is equal to:

2250/10 = 225 cm
or
2.25 m

2.2 The sum of all the angles of a regular n-gon is equal to:
180° * (n - 2)
where n is the number of sides of a regular polygon
Then
2160 = 180° * (n - 2)
12 = n - 2
n = 12 + 2 = 14
So the polygon has 14 sides

2.3 The total surface area of ​​the cylinder is the sum of the areas of the side surface and the bases.
S = S1 + S2
The area of ​​the lateral surface of the cylinder is equal to the product of the circumference by the height of the cylinder.
S1 = 2пr * h = 2 * 3.14 * 14 * 20 = 1758.4 cm ^ 2 
The area of ​​the bases is equal to the area of ​​the circumference. The cylinder has two bases, so the area of ​​the circumference is multiplied by 2
S2 = 2 * пr^2 = 2 * 3.14 * 14 ^ 2 =  1230.88 cm ^ 2 
Then the total area of ​​the cylinder is:
S = S1 + S2 = 1758.4 + 1230.88 = 2989.28 cm ^ 2

Answer:2.1 The length of each side of the regular decagonal field is 2.25 m
       2.2 So a regular polygon is a 14-gon
       2.3 The total surface area of ​​the cylinder is 2989.28 cm ^ 2