Solved Examples on Polygon in Maths
Example 1: Consider a quadrilateral with four sides. Find the sum of all its interior angles of quadrilateral.
Solution:
Formula for the sum of interior angles in an n-sided regular polygon = (n − 2) × 180°
The sum of all the interior angles of the quadrilateral = (4 – 2) × 180°
The sum of all the interior angles of the quadrilateral = 2 × 180°
The sum of all the interior angles of the quadrilateral = 360°
Therefore, the sum of all the interior angles of the quadrilateral is 360°.
Example 2: Consider a Regular Polygon with a given exterior and interior angle ratio of 7:3. Determine the type of polygon.
Solution:
The ratio of the exterior and interior angle is 7:3.
Assume the exterior and interior angle of a polygon as 7x and 3x.
The sum of the exterior and interior angles of any polygon is 180°.
7x + 3x = 180°
10x = 180°
x = 18°
Exterior angle = 18°
Number of sides = 360°/exterior angle
= 360°/18°
= 20
Therefore, the given polygon is an icosagon, as it has 20 sides.
Example 3: Each Exterior Angle of a Polygon measures 90 degrees, determine the type of Polygon?
Solution:
As per the formula, each exterior angle = 360°/n
Here n=number sides.
90°= 360°/n
n = 360°/90°= 4
Hence, the Polygon in question is a quadrilateral, as it possesses four sides.
Example 4: The sides are 10m, 10m, 8m, 8m, 5m, 5m, 9m, 9m. How many meters of rope will be needed for the Perimeter?
Solution:
In order to find the length of the rope needed for the perimeter, we must sum the lengths of all the sides:
Perimeter = 10 m + 10 m + 8 m + 8 m + 5 m + 5 m + 9 m + 9 m
Perimeter = 64 m.
Therefore, a total of 64 meters of rope will be needed for the Perimeter.
Polygon – Shape, Formula, Types, and Examples
Polygon in Maths is a two-dimensional shape made up of straight lines that form a closed polygonal chain. The word “polygon” comes from the words “poly” and “gon”, which mean “many” and “sides”.
Polygons can be simple or self-intersecting. A simple polygon does not intersect itself, except at the shared endpoints of consecutive segments. A polygonal chain that crosses over itself creates a self-intersecting polygon. Polygons can also be classified as concave or convex.
In this article, we have mentioned in detail about Polygons and their types, formulas, and examples.
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Important Facts about Polygons |
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|---|---|
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Sum of Interior Angles of Polygon |
(n–2) × 180° |
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Number of Diagonals in Polygon |
n(n–3)/2 |
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Interior Angle of Regular Polygon |
{(n–2) × 180°}/n |
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Exterior Angle of Regular polygon |
360°/n |
Table of Content
- What are Polygons?
- Polygon Definition
- Polygon Chart based on Number of Sides
- Properties of Polygons
- Polygon Shapes
- Types of Polygons
- Polygons on the Basis of Sides
- Polygons On Basis of Angles
- Polygons On Basis of Boundaries
- Polygon Formulas
- Area of Polygons
- Perimeter of Polygons
- Angles in Polygons
- FAQs
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