In this lesson you’ll learn about the concepts of Perimeter of Polygons,
and how
to find the perimeter there of. The presentation covering such content will be done
by the instructor in own handwriting, using video and with the help of several examples
with solution. This will help you understand and master the formulas of important
geometry applications in this area, and how to apply them to find solution.
Perimeter of Polygons: is the measurement of the distance around the outside of
the polygon i.e. the perimeter of a polygon is the sum of the lengths of all its
sides. E.g. in the figure below; you can see an irregular hexagon
(A, B, C, D, E,
F), whose perimeter is:
(4 cm + 4cm + 4cm +4cm + 5cm + 5cm) = 26 cm.
(Continued from above)
In case of ‘Regular Polygon’; meaning whose sides are equal and also all the angles are equal,
perimeter can be determined by “length of the side x number of sides”. For example, perimeter
of a Pentagon (5 sides polygon), is 5 times length of side and in case of Heptagon
(7 sides polygon), the perimeter is 7 times length of side.
Perimeter of Polygons: Summary
Figure
Polygon
Perimeter/Circumference
Square
4a
Rectangle
2l + 2w or 2(l + w)
Parallelogram
2a + 2b or 2(a + b)
Triangle
(a + b + c)
Trapezoid
(a + b1 + c + b2)
Regular Polygon
ns n = number of sides
Circle
* d
or 2 * * r
You can explore now how the concepts can be applied to solve the problems using
relationship and properties of polygons. For example:
Given: a regular hexagon in inscribed in a circle of radius 10 cm. You are to find
out the perimeter of this hexagon.
As learnt earlier, hexagon is six sides polygon. Draw a diagram a below:
•
AOP is found out by,
AOP =
360 / 6 =
60
(it is six sided regular polygon)
•
As OA = OP = 10 cm, OAP is isosceles, and thus
OAP =
OPA
Therefore, all three angles of the triangle are equal and it is an equilateral triangle. Hence
AP = OA = OP = 10 cm.
As it is a six sided polygon, thus perimeter of the polygon is 6*10 = 60 cm, as the final answer.
The video above will explain more in detail
about Perimeter of Polygons,
with the help of several examples.
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